BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Collorg//www.collorg.org CALSCALE:GREGORIAN BEGIN:VEVENT SUMMARY:Stéphane Bessy\, «Extremal values of the chromatic number for a given degree sequence» DTSTART;VALUE=DATE-TIME:20170126T090000Z DTEND;VALUE=DATE-TIME:20170126T100000Z DTSTAMP;VALUE=DATE-TIME:20170105T124224Z UID:ae90c54a-11c3-4649-9e2d-1187903bae82 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20170105T124224Z DESCRIPTION:joint work with D. Rautenbach (Ulm University\, Germany)\n\n\n Pour une séquence de degrés d: d1 >= d2 >= ... >= dn\, on définit Xmax( d) (resp. Xmin(d)) le plus grand (resp. plus petit) nombre chromatique d' un graphe de séquence de degrés d.\n\nAprès avoir motivé l'étude de c es invariants (d'un point de vue théorique ainsi qu'applicatif -hum...-)\ , puis présenté les grands résultats connus sur les réalisations de s équences de degrés\, je donnerai les résultats théoriques et algorithm iques que nous avons obtenus pour borner ou calculer Xmax et Xmin. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/ae90c54a-11c3-4649-9e2d-1187903bae82 END:VEVENT BEGIN:VEVENT SUMMARY:Mickael Montassier\, «3-paths with given degree sequence» DTSTART;VALUE=DATE-TIME:20141211T090000Z DTEND;VALUE=DATE-TIME:20141211T103000Z DTSTAMP;VALUE=DATE-TIME:20141204T180630Z UID:f9096f03-2653-486f-81a5-12de5ce4efd0 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20141204T180630Z DESCRIPTION:In this talk\, we present results on the existence of paths of length 3 with given degree sequence in sparse graphs.\n\nJoint work with S. Jendrol\, M. Macekova\, and R. Sotak. LAST-MODIFIED;VALUE=DATE-TIME:20141210T090104Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/f9096f03-2653-486f-81a5-12de5ce4efd0 END:VEVENT BEGIN:VEVENT SUMMARY:Luis Pedro Montejano\, «Transversals to the convex hulls of all k -sets of discret substets of R^d» DTSTART;VALUE=DATE-TIME:20150528T080000Z DTEND;VALUE=DATE-TIME:20150528T093000Z DTSTAMP;VALUE=DATE-TIME:20150225T142107Z UID:e8d6efb5-f1fd-46ee-9123-e54191648bb0 SEQUENCE:6 CREATED;VALUE=DATE-TIME:20150225T142107Z DESCRIPTION:Let $k\,d\,\\lambda$ be positive integers with $d\\ge\\lambda$ . We investigate the following two questions. What is the maximum positive integer $n$ such that every set of $n$ points in $\\mathbb{R}^d$ has a (k neser) transversal $(d-\\lambda)$-plane intersecting the convex hulls of a ll $k$-sets ? What is the minimum positive integer $n$ such that every set of $n$ points in general position in $\\mathbb{R}^d$ there is no (kneser) transversal $(d-\\lambda)$-plane intersecting the convex hulls of all $k$ -sets ? A transversal $(d-\\lambda)$-Plane in $\\mathbb{R}^d$ is an affine subspace of dimension $d-\\lambda$. A kneser transversal $(d-\\lambda)$-p lane for a set of points $S$ in $\\mathbb{R}^d$ is an affine subspace of d imension $d-\\lambda$ that goes through $d-\\lambda+1$ points of $S$. Firs t question is related with Kneser hypergraph and its chromatic number (whe n $\\lambda=1$\, it is equivalent to Kneser's conjecture). We will see how answering first question could give improvements to this problem. LAST-MODIFIED;VALUE=DATE-TIME:20150609T121754Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/e8d6efb5-f1fd-46ee-9123-e54191648bb0 END:VEVENT BEGIN:VEVENT SUMMARY:Pascal Ochem\, «Homomorphism of 2-edge-colored and 2-vertex-color ed graphs» DTSTART;VALUE=DATE-TIME:20150205T090000Z DTEND;VALUE=DATE-TIME:20150205T103000Z DTSTAMP;VALUE=DATE-TIME:20150116T175346Z UID:9556c085-eb5f-4137-8cc6-95e26ccbe7dd SEQUENCE:3 CREATED;VALUE=DATE-TIME:20150116T175346Z DESCRIPTION:The CSP dichotomy conjecture is that every constraint satisfac tion problem is polynomial or NP-complete. Feder and Vardi have shown that the CSP conjecture can be reduced to the case of digraph homomorphism. He ll and Nesetril settled the complexity of homomorphism to a graph G: it is polynomial if G is bipartite and NP-complete otherwise. We will show that the CSP conjecture can be reduced to the case of 2-edge-colored homomorph ism and to the case of 2-vertex-colored homomorphism (also known as tropic al homomorphism).\n\nIt is a joint work with Nazanin Movarraei. LAST-MODIFIED;VALUE=DATE-TIME:20150204T090102Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/9556c085-eb5f-4137-8cc6-95e26ccbe7dd END:VEVENT BEGIN:VEVENT SUMMARY:Guillem Perarnau\, «Edge-decompositions of graphs with maximum bo unded degree» DTSTART;VALUE=DATE-TIME:20141218T090000Z DTEND;VALUE=DATE-TIME:20141218T103000Z DTSTAMP;VALUE=DATE-TIME:20141117T154146Z UID:402c224c-74b4-4c78-8472-e483370e954b SEQUENCE:1 CREATED;VALUE=DATE-TIME:20141117T154146Z DESCRIPTION:In this talk I will introduce two problems on edge-decompositi ons of graphs with bounded maximum degree. First\, I will present a new ap proach to acyclic edge colorings of graphs with large girth. Using it\, we obtain asymptotically tight results on a conjecture of Alon\, Sudakov and Zaks. In the second part I will talk about the problem of partitioning th e edges of a graph in different improper color classes with no monochromat ic copy of a fixed graph. I will present an iterative embedding argument t hat allows us to transfer classical results from Extremal Graph Theory to bounded degree graphs. The common denominator of these two topics is the u se of the so-called semirandom method. All the presented results are joint work with Cai\, Reed and Watts (Part 1) and with Foucaud\, Kang\, Krivele vich and Reed (Part 2). LAST-MODIFIED;VALUE=DATE-TIME:20141217T090103Z LOCATION:E.3.23\, LIRMM URL:https://info-web.lirmm.fr/collorg/402c224c-74b4-4c78-8472-e483370e954b END:VEVENT BEGIN:VEVENT SUMMARY:Ignasi Sau\, «On the complexity of computing the k-restricted edg e-connectivity of a graph» DTSTART;VALUE=DATE-TIME:20150611T080000Z DTEND;VALUE=DATE-TIME:20150611T093000Z DTSTAMP;VALUE=DATE-TIME:20150422T121843Z UID:cd27e500-3bde-45aa-b7db-f4e08220600d SEQUENCE:7 CREATED;VALUE=DATE-TIME:20150422T121843Z DESCRIPTION:The //$k$-restricted edge-connectivity// of a graph $G$\, deno ted by $\\lambda_k(G)$\, is defined as the minimum size of an edge set who se removal leaves exactly two connected components each containing at leas t $k$ vertices. This graph invariant\, which can be seen as a generalizati on of a minimum edge-cut\, has been extensively studied from a combinatori al point of view. However\, very little is known about the complexity of c omputing $\\lambda_k(G)$. Very recently\, in the parameterized complexity community the notion of //good edge separation// of a graph has been defin ed\, which happens to be essentially the same as the $k$-restricted edge-c onnectivity. Motivated by the relevance of this invariant from both combin atorial and algorithmic points of view\, we initiate a systematic study of its computational complexity\, with special emphasis on its parameterized complexity for several choices of the parameters. We provide a number of NP-hardness and W[1]-hardness results\, as well as FPT-algorithms.\n\nThis is joint work with Luis P. Montejano. LAST-MODIFIED;VALUE=DATE-TIME:20150610T080103Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/cd27e500-3bde-45aa-b7db-f4e08220600d END:VEVENT BEGIN:VEVENT SUMMARY:O-joung Kwon\, «A fixed parameter tractable algorithm for linear rank-width using the obstruction set» DTSTART;VALUE=DATE-TIME:20150129T090000Z DTEND;VALUE=DATE-TIME:20150129T103000Z DTSTAMP;VALUE=DATE-TIME:20150127T125501Z UID:0703fcbe-72a9-49ba-ba28-eb2c2f2d6033 SEQUENCE:2 CREATED;VALUE=DATE-TIME:20150127T125501Z DESCRIPTION:We first give a brief introduction of rank-width and linear ra nk-width. Even though rank-width has been well developed by a series of pa pers\, only few known algorithmic or structural properties are developed f or linear rank-width until recently. We list some problems related to this area\, and then focus on a fixed parameter tractable algorithm using the obstruction set for bounded linear rank-width. We mainly show that the num ber of pivot-minor obstructions for linear rank-width at most k is doubly exponential in O(k). LAST-MODIFIED;VALUE=DATE-TIME:20150128T130103Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/0703fcbe-72a9-49ba-ba28-eb2c2f2d6033 END:VEVENT BEGIN:VEVENT SUMMARY:Benjamin Lévêque\, «Structure of Schnyder labelings on orientab le surfaces» DTSTART;VALUE=DATE-TIME:20141204T090000Z DTEND;VALUE=DATE-TIME:20141204T103000Z DTSTAMP;VALUE=DATE-TIME:20141117T153928Z UID:0101fb62-4c8c-4f08-89c4-932f61e55fb3 SEQUENCE:3 CREATED;VALUE=DATE-TIME:20141117T153928Z DESCRIPTION:We propose a simple generalization of Schnyder woods to higher genus. We give a necessary and sufficient condition for an orientation to corresponds to such a Schnyder wood and we study the relations between th ese orientations. Unfortunately we are not able to prove the existence of these Schnyder woods in general but a new proof for the toroidal case is d erived from this study. LAST-MODIFIED;VALUE=DATE-TIME:20141203T124603Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/0101fb62-4c8c-4f08-89c4-932f61e55fb3 END:VEVENT BEGIN:VEVENT SUMMARY:Mordo Shalom\, «A Polynomial-time Algorithm for the Maximum Cardi nality Cut Problem in Proper Interval Graphs» DTSTART;VALUE=DATE-TIME:20170223T090000Z DTEND;VALUE=DATE-TIME:20170223T100000Z DTSTAMP;VALUE=DATE-TIME:20170222T090201Z UID:87fc5471-3d8d-4f5d-9101-51cd1f32c35c SEQUENCE:2 CREATED;VALUE=DATE-TIME:20170222T090201Z DESCRIPTION:It is known that the maximum cardinality cut problem is NP-har d even in chordal graphs. On the positive side\, the problem is known to b e polynomial time solvable in some subclasses of proper interval graphs wh ich is in turn a subclass of chordal graphs. In this paper\, we consider t he time complexity of the problem in proper interval graphs\, and propose a polynomial-time dynamic programming algorithm. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/87fc5471-3d8d-4f5d-9101-51cd1f32c35c END:VEVENT BEGIN:VEVENT SUMMARY:Guilherme D. da Fonseca\, «Approximate Polytope Membership Querie s» DTSTART;VALUE=DATE-TIME:20150226T090000Z DTEND;VALUE=DATE-TIME:20150226T103000Z DTSTAMP;VALUE=DATE-TIME:20150115T123419Z UID:d51e8486-0504-481c-9974-01329b53ec46 SEQUENCE:5 CREATED;VALUE=DATE-TIME:20150115T123419Z DESCRIPTION:We consider an approximate version of a fundamental geometric search problem\, polytope membership queries. Given a convex polytope P in d-dimensional space\, presented as the intersection of halfspaces\, the o bjective is to preprocess P so that\, given a query point q\, it is possib le to determine efficiently whether q lies inside P subject to an allowed error ε. Previous solutions to this problem were based on straightforward applications of classic polytope approximation techniques by Dudley (1974 ) and Bentley et al. (1982). The former yields minimum storage\, the latte r yields constant query time\, and a space-time tradeoff can be obtained b y interpolating between the two.\n\nWe present the first significant impro vements to this tradeoff. For example\, using the same storage as Dudley\, we reduce the query time from O(1/ε^(d-1)/2) to O(1/ε^(d-1)/4) and\, us ing a more involved analysis\, to O(1/ε^(d-1)/8). Our approach is based o n a very simple construction algorithm\, whose analysis is surprisingly no ntrivial. Both lower bounds and upper bounds on the performance of the alg orithm are presented. For the same storage as Dudley\, we present a lower bound of Ω(1/ε^(d-1)/18).\n\nTo establish the relevance of our results\, we introduce a reduction from approximate nearest neighbor searching to a pproximate polytope membership queries. Remarkably\, we show that our trad eoff provides significant improvements to the best known space-time tradeo ffs for this very well studied problem.\n\nThis is joint work with Sunil A rya and David M. Mount. LAST-MODIFIED;VALUE=DATE-TIME:20150521T092215Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/d51e8486-0504-481c-9974-01329b53ec46 END:VEVENT BEGIN:VEVENT SUMMARY:Arnau Padrol\, «Realizations of neighborly\, inscribable and egg- scribable polytopes» DTSTART;VALUE=DATE-TIME:20141120T090000Z DTEND;VALUE=DATE-TIME:20141120T103000Z DTSTAMP;VALUE=DATE-TIME:20141117T153242Z UID:abc8cce9-00a8-4d8f-9b89-ff34c3d05c3d SEQUENCE:5 CREATED;VALUE=DATE-TIME:20141117T153242Z DESCRIPTION:Delaunay triangulations in R^d are a central object in many ar eas of mathematics and computational geometry. However\, little is known a bout which combinatorial types can appear as a Delaunay triangulation. Wit h an inverse stereographic projection\, this question translates to asking which combinatorial types of polytopes admit realizations with all the ve rtices on a d-sphere. We will construct a large family of neighborly polyt opes that are not only inscribable on the sphere\, but also in every smoot h strictly convex body. This provides the current best lower bound for the number of combinatorial types of Delaunay triangulations. In the second p art of the talk\, we will use these techniques to show that realization sp aces of inscribed polytopes present Universality in the sense of Mnëv. Fo r example\, this will allow us to construct a pair of point configurations whose Delaunay triangulations are combinatorially equivalent but yet ther e is no continuous transformation that maps one to the other without chang ing the combinatorics of the Delaunay triangulation. \n\nThis talk reports joint work with Karim Adiprasito\, Bernd Gonska and Louis Theran. LAST-MODIFIED;VALUE=DATE-TIME:20141119T101558Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/abc8cce9-00a8-4d8f-9b89-ff34c3d05c3d END:VEVENT BEGIN:VEVENT SUMMARY:réunion DEMOGRAPH\, «TBA» DTSTART;VALUE=DATE-TIME:20170919T080000Z DTEND;VALUE=DATE-TIME:20170919T090000Z DTSTAMP;VALUE=DATE-TIME:20170830T081634Z UID:bfa06fda-3122-4d2b-9070-f50446e3f621 SEQUENCE:0 CREATED;VALUE=DATE-TIME:20170830T081634Z DESCRIPTION:TBA LAST-MODIFIED;VALUE=DATE-TIME:20170830T083105Z LOCATION: URL:https://info-web.lirmm.fr/collorg/bfa06fda-3122-4d2b-9070-f50446e3f621 END:VEVENT BEGIN:VEVENT SUMMARY:Dimitrios M. Thilikos\, «Linkages and cyclic linkages» DTSTART;VALUE=DATE-TIME:20150521T080000Z DTEND;VALUE=DATE-TIME:20150521T093000Z DTSTAMP;VALUE=DATE-TIME:20150304T153908Z UID:f67a6143-8937-4acd-81ec-b553a3bd414c SEQUENCE:5 CREATED;VALUE=DATE-TIME:20150304T153908Z DESCRIPTION:The cyclability of a graph is the maximum integer $k$ for whic h every $k$ vertices lie on a cycle. The algorithmic version of the prob lem\, given a graph $G$ and a non-negative integer $k\,$ decide whether th e cyclability of $G$ is at least $k\,$ is NP-hard. We study the parametriz ed complexity of this problem. We prove that this problem\, parameterized by $k\,$ is W[1]-hard and that its does not admit a polynomial kernel on p lanar graphs\, unless $NP\\subseteq coNP/poly$. On the positive side\, we give an FPT algorithm for planar graphs that runs in time $2^{2^{O(k^2\\l og k)}}\\cdot n^2$. Our algorithm is based on a series of graph-theoretica l results on cyclic linkages in planar graphs. The algorithm is based on c ombinatorial results on linkages and cyclic linkages on planar graphs.\n\n Joint work with Petr A. Golovach\, Marcin Kamiński\, and Spyridon Maniati s. LAST-MODIFIED;VALUE=DATE-TIME:20150520T080102Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/f67a6143-8937-4acd-81ec-b553a3bd414c END:VEVENT BEGIN:VEVENT SUMMARY:Céline Scornavacca\, «(Strict) compatibility of unrooted phyloge netic trees» DTSTART;VALUE=DATE-TIME:20141127T090000Z DTEND;VALUE=DATE-TIME:20141127T103000Z DTSTAMP;VALUE=DATE-TIME:20141016T120619Z UID:b0794113-bdcf-459a-aabc-063cc91982a8 SEQUENCE:6 CREATED;VALUE=DATE-TIME:20141016T120619Z DESCRIPTION:A collection F of k unrooted phylogenetic trees on different l eaf sets is said to be compatible if there exists a tree T such that each tree in F can be obtained from T by deleting leaves\, suppressing degree- 2 vertices\, and by contracting edges. In the case of strict compatibility \, the latter operation is not permitted. \nThe problem of determining if a set of unrooted trees is (strictly) compatible has been proved NP-hard in 1992. In this seminar\, I will use Monadic Second Order (MSO) logic to prove that an f(k)·n algorithm for these problems exists\, for some compu table function f of k\, proving that (strict) compatibility of unrooted ph ylogenetic trees is fixed-parameter tractable with respect to the number k of trees. Designing a practical FPT algorithm remains an open problem.\nI f time\, I will give alternative\, compact proofs of fixed parameter tract ability for the computation of several well-known incongruency parameters in phylogenetics\, ie the rSPR distance. LAST-MODIFIED;VALUE=DATE-TIME:20141126T090103Z LOCATION:E.2.23 URL:https://info-web.lirmm.fr/collorg/b0794113-bdcf-459a-aabc-063cc91982a8 END:VEVENT BEGIN:VEVENT SUMMARY:Julien Baste\, «Parameterized complexity dichotomy for (r\,l)-Ver tex Deletion» DTSTART;VALUE=DATE-TIME:20150625T080000Z DTEND;VALUE=DATE-TIME:20150625T093000Z DTSTAMP;VALUE=DATE-TIME:20150422T122039Z UID:caffd1a1-61d7-4d90-bdc4-ddba397ef58a SEQUENCE:3 CREATED;VALUE=DATE-TIME:20150422T122039Z DESCRIPTION:For two integers $r\, \\ell \\geq 0$\, a graph $G = (V\, E)$ i s an $(r\,\\ell)$-graph if $V$ can be partitioned into $r$ independent set s and $\\ell$ cliques. In the parameterized $(r\,\\ell)$-Vertex Deletion p roblem\, given a graph $G$ and an integer $k$\, one has to decide whether at most $k$ vertices can be removed from $G$ to obtain an $(r\,\\ell)$-gra ph. This problem is NP-hard if $r+\\ell \\geq 1$ and encompasses several r elevant problems such as Vertex Cover and Odd Cycle Transversal. The param eterized complexity of $(r\,\\ell)$-Vertex Deletion was known for all valu es of $(r\,\\ell)$ except for $(2\,1)$\, $(1\,2)$\, and $(2\,2)$. We prove that each of these three cases is FPT and\, furthermore\, solvable in sin gle-exponential time\, which is asymptotically optimal in terms of $k$. We consider as well the version of $(r\,\\ell)$-Vertex Deletion where the se t of vertices to be removed has to induce an independent set\, and provide also a parameterized complexity dichotomy for this problem.\n\nThis is jo int work with Luerbio Faria\, Sulamita Klein\, and Ignasi Sau. LAST-MODIFIED;VALUE=DATE-TIME:20150624T080103Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/caffd1a1-61d7-4d90-bdc4-ddba397ef58a END:VEVENT BEGIN:VEVENT SUMMARY:Christophe Paul\, «Rankwidth vertex deletion» DTSTART;VALUE=DATE-TIME:20150305T090000Z DTEND;VALUE=DATE-TIME:20150305T103000Z DTSTAMP;VALUE=DATE-TIME:20150225T141636Z UID:5b882025-f363-4d55-8388-bdb10b400198 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20150225T141636Z DESCRIPTION:Le problème Rankwidth-c Vertex Deletion consiste à supprimer k sommets pour obtenir un graphe de ranwkdith au plus c\, où c est une c onstante. Ce problème est non-uniforme FPT paramétré par k. La question posée est de savoir si ce problème peut être résolu en temps FPT simp le exponentiel. Le cas c=1 est intéressant pour plusieurs raisons. Il cor respond au problème Distance Hereditary Graphs Vertex Deletion et est l'a nalogue pour la treewidth au problème Feedback Vertex Set. Nous répondon s positivement à la question et montrons l’existence d’un noyau polyn omial pour les graphes de rankwidth linéaire 1.\n\nCo-auteurs: M. Kanté (LIMOS)\, E.J. Kim (LAMSADE)\, O. Kwon (KAIST\, Korea). LAST-MODIFIED;VALUE=DATE-TIME:20150609T093902Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/5b882025-f363-4d55-8388-bdb10b400198 END:VEVENT BEGIN:VEVENT SUMMARY:Ignasi Sau\, «FPT algorithm for a generalized cut problem and som e applications» DTSTART;VALUE=DATE-TIME:20150115T090000Z DTEND;VALUE=DATE-TIME:20150115T103000Z DTSTAMP;VALUE=DATE-TIME:20150105T170213Z UID:9c6c1311-bf21-4dc0-89cc-f434c21a8e12 SEQUENCE:3 CREATED;VALUE=DATE-TIME:20150105T170213Z DESCRIPTION:In this talk we will sketch an FPT algorithm for a quite gener al cut problem on general graphs\, which we call List Allocation. Our algo rithm strongly uses the "edge contraction" technique introduced by Chitnis et al. [2012]. Besides being a natural cut problem by itself\, the relev ance of List Allocation is best demonstrated by the following algorithms\, which we obtain by reducing in FPT time each corresponding problem to par ticular cases of List Allocation: \n\n(1) An FPT algorithm for a generaliz ation of Digraph Homomorphism\, which we call Arc-Bounded List Digraph Hom omorphism.\n(2) An FPT algorithm for a graph partitioning problem\, which we call Min-Max Graph Partitioning.\n(3) An FPT 2-approximation algorithm for computing the "tree-cut width" of a graph\, a graph invariant recently introduced by Wollan [2013] and that has proved of fundamental importance in the structure of graphs not admitting a fixed graph as an immersion.\n \nIf time permits\, we will partially discuss the above applications of ou r main algorithm.\n\nThis is joint work with EunJung Kim\, Sang-Il Oum\, C hristophe Paul\, and Dimitrios M. Thilikos. LAST-MODIFIED;VALUE=DATE-TIME:20150114T090104Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/9c6c1311-bf21-4dc0-89cc-f434c21a8e12 END:VEVENT BEGIN:VEVENT SUMMARY:Vincent Despré\, «Les différentes notions de simplicité\, cas particulier du cycle de partage» DTSTART;VALUE=DATE-TIME:20150402T080000Z DTEND;VALUE=DATE-TIME:20150402T093000Z DTSTAMP;VALUE=DATE-TIME:20150211T134042Z UID:b460611c-e571-4c1b-94fb-397c52d7b1f0 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20150211T134042Z DESCRIPTION:On s'intéresse aux graphes plongés sur des surfaces. Dès qu 'on considère une surface plus compliquée que le plan ou la sphère des problèmes topologiques apparaissent. Beaucoup de travaux on été réalis és dans un cadre purement mathématiques sur le sujet y compris des trava ux de nature algorithmique. Cependant les algorithmes proposés ne sont pa s réellement utilisables en général. Certaines notions comme la simplic ité sont problématiques. Effectivement\, on obtient beaucoup plus facile ment une courbe simple (sans point double) sur la surface qu'un cycle simp le (sans sommet répété) dans un graphe plongé. On s'intéressera en pa rticulier à la recherche de cycles simples (au sens du graphe) qui permet tent de découper la surface sous-jacente en 2 parties non-planaires i.e. les cycles de partage. LAST-MODIFIED;VALUE=DATE-TIME:20150402T092713Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/b460611c-e571-4c1b-94fb-397c52d7b1f0 END:VEVENT BEGIN:VEVENT SUMMARY:Claire Hilaire\, «Graph Major of Graph Drawing» DTSTART;VALUE=DATE-TIME:20210902T080000Z DTEND;VALUE=DATE-TIME:20210902T090000Z DTSTAMP;VALUE=DATE-TIME:20210728T104332Z UID:5a38f922-a8b0-4ad2-9129-dd6f2a1164ed SEQUENCE:1 CREATED;VALUE=DATE-TIME:20210728T104332Z DESCRIPTION:Motivated by the Grid-Minor Theorem of Robertson and Seymour\, a.k.a. the Excluded Grid Theorem\, we study the following problem on the relation between graph drawings and grid minors: //for any given planar gr aph $H$ with a polyline drawing on a $p\\times q$ grid\, what is the small est area $A = A(p\,q)$ of a grid having $H$ as minor//?\n\nSince $H$ is a planar graph with at most $pq$ vertices\, a classical result in Graph Mino r Theory implies that $H$ is minor of a square grid of side $2pq-4$\, yiel ding the upper bound $A(p\,q) = O( (pq)^2 )$. More recently\, Dieng and Ga voille showed that $A(p\,q) = O(p^2 q)$\, leaving open the question whethe r $A(p\,q) = O(p q)$ or not. This upper bound would be optimal since clear ly $A(p\,q) \\ge pq$ if $H$ is a $p \\times q$ grid.\n\nIn this study\, we proved that finding the smallest area of a grid having $H$ as minor is NP -hard\, and also that $A(p\,q) = O(pq)$ holds for several large classes of $n$-vertex planar graphs with dense drawing\, i.e.\, with drawing area $O (n)$. LAST-MODIFIED;VALUE=DATE-TIME:20210901T080102Z LOCATION:https://bbb.lirmm.fr/b/dim-ajj-ddd URL:https://info-web.lirmm.fr/collorg/5a38f922-a8b0-4ad2-9129-dd6f2a1164ed END:VEVENT BEGIN:VEVENT SUMMARY:Stéphane Bessy\, «Antistrong digraphs» DTSTART;VALUE=DATE-TIME:20150409T080000Z DTEND;VALUE=DATE-TIME:20150409T093000Z DTSTAMP;VALUE=DATE-TIME:20150225T141733Z UID:16ce8e8c-27ed-4c82-b484-a54cc6551621 SEQUENCE:2 CREATED;VALUE=DATE-TIME:20150225T141733Z DESCRIPTION:Pour d'obscures raisons\, nous définissons la notion de graph e orienté\nantistrong (par opposition à strong -fortement connexe-). Un graphe orienté\nest antistrong si tout couple de points peut être relié par un parcours orienté alternant.\nLa (bonne) caractérisation d'un gra phe antistrong est que son graphe biparti\nd'incidence est connexe.\nOn s' est intéressé principalement à des questions algorithmiques autour\nde cette notion. Certaines découlent facilement de la caractérisation préc édente\,\nd'autres sont plus difficiles à établir. Des techniques matro ïdales ont notamment\nété utiles pour obtenir certains résultats.\n\nD ans cet exposé\, je motiverai et présenterai ces différents résultats. J'en profiterai pour\nfaire aussi le tour de quelques outils de matroïde s pour graphes qui\, bien que pas\nrécents\, m'ont enthousiasmé récemme nt...\n\nTravail commun avec J. Bang-Jensen\, B. Jackson et M. Kriessell. LAST-MODIFIED;VALUE=DATE-TIME:20150408T080104Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/16ce8e8c-27ed-4c82-b484-a54cc6551621 END:VEVENT BEGIN:VEVENT SUMMARY:Julien Bensmail\, «Strong edge-coloring of $(3\,\\Delta)$-biparti te graphs» DTSTART;VALUE=DATE-TIME:20150312T090000Z DTEND;VALUE=DATE-TIME:20150312T103000Z DTSTAMP;VALUE=DATE-TIME:20150226T162602Z UID:f3150ac4-497d-4a7c-9689-04f69ce6767c SEQUENCE:7 CREATED;VALUE=DATE-TIME:20150226T162602Z DESCRIPTION:An edge-coloring of a graph $G$ is strong if its every color c lass is an induced matching. The strong chromatic index of $G$\, denoted $ \\chi'_s(G)$\, is the least number of colors in a strong edge-coloring of $G$. Greedy coloring arguments show that $\\chi'_s$ is bounded above by ro ughly $2\\Delta^2$\, where $\\Delta$ denotes the maximum degree of an impl icit graph\, though this upper bound is not reached in general. A long-sta nding conjecture of Erdös and Nešetřil (1989) states that the right up per bound on the strong chromatic index should actually be roughly $1.25\\ Delta^2$\, which would be tight as confirmed by a particular family of gra phs with a lot of small cycles ($C_4$'s and $C_5$'s). Excluding small cycl es (i.e. with length at most $5$) in a graph is expected to make the stron g chromatic index be smaller\, as confirmed notably by Mahdian (2000) for $C_4$-free graphs. This observation made Faudree\, Gyárfás\, Schelp and Tuza (1990) conjecture that the strong chromatic index of bipartite graphs (which have no $C_3$'s and $C_5$'s) should be bounded above by $\\Delta^2 $. In the continuity of previous results of Steger and Yu (1993) and Nakpr asit (2008)\, we verify this conjecture for bipartite graphs whose one par t is of maximum degree at most~$3$.\n\nThis is a joint work with A. Lagout te and P. Valicov. LAST-MODIFIED;VALUE=DATE-TIME:20150312T131229Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/f3150ac4-497d-4a7c-9689-04f69ce6767c END:VEVENT BEGIN:VEVENT SUMMARY:Tereza Klimošová\, «Infinite dimensional finitely forcible grap hon» DTSTART;VALUE=DATE-TIME:20150212T090000Z DTEND;VALUE=DATE-TIME:20150212T103000Z DTSTAMP;VALUE=DATE-TIME:20150202T193823Z UID:0eb9e8f6-2884-4ab5-a79e-c2749a912961 SEQUENCE:0 CREATED;VALUE=DATE-TIME:20150202T193823Z DESCRIPTION:Graphons are analytic objects associated with convergent seque nces of graphs. Problems from extremal combinatorics and theoretical compu ter science led to a study of graphons determined by finitely many subgrap h densities\, which are referred to as finitely forcible. We show that th ere exists a finitely forcible graphon such that the topological space of its typical vertices has infinite Lebesgue covering dimension\, disproving the conjecture by Lovasz and Szegedy. The talk is based on joint work wit h Roman Glebov and Dan Král'. LAST-MODIFIED;VALUE=DATE-TIME:20150211T090104Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/0eb9e8f6-2884-4ab5-a79e-c2749a912961 END:VEVENT BEGIN:VEVENT SUMMARY:Mathieu Liedloff\, «Minimal dominating sets on some graph classes : combinatorial upper bounds and enumeration» DTSTART;VALUE=DATE-TIME:20150326T090000Z DTEND;VALUE=DATE-TIME:20150326T103000Z DTSTAMP;VALUE=DATE-TIME:20150202T175626Z UID:a323ab9f-5d07-4f37-bd76-dae58d202339 SEQUENCE:11 CREATED;VALUE=DATE-TIME:20150202T175626Z DESCRIPTION:Given a graph $G=(V\,E)$\, a subset $D$ of vertices is a domin ating set if each vertex is either in $D$ or has at least one neighbor in $D$. A dominating set is minimal if it contains no dominating set as a pro per subset.\n\nAn interesting question is to determine the maximum number of minimal dominating sets in a graph. In this talk we provide upper bound s on this maximum number for various graph classes (split\, cobipartite an d interval graphs). These bounds are established via the running-time anal ysis of exponential-time algorithms which enumerates all the minimal domin ating sets. LAST-MODIFIED;VALUE=DATE-TIME:20150609T093829Z LOCATION:de séminaire (EXCEPTIONNELLEMENT)\, en RDC à côté de l'accuei l URL:https://info-web.lirmm.fr/collorg/a323ab9f-5d07-4f37-bd76-dae58d202339 END:VEVENT BEGIN:VEVENT SUMMARY:Mickael Montassier\, «Cycles and Colourings: problem session» DTSTART;VALUE=DATE-TIME:20140918T080000Z DTEND;VALUE=DATE-TIME:20140918T090000Z DTSTAMP;VALUE=DATE-TIME:20150201T014751Z UID:3f82ab9f-c83c-4392-818b-2f6585271c93 SEQUENCE:0 CREATED;VALUE=DATE-TIME:20150201T014751Z DESCRIPTION:Cet exposé sera la présentation des problèmes ouverts posé s lors du workshop "Cycles and Colourings 2014". LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/3f82ab9f-c83c-4392-818b-2f6585271c93 END:VEVENT BEGIN:VEVENT SUMMARY:Gabriel Renault\, «Misère Geography and Vertex NimG are pspace-h ard» DTSTART;VALUE=DATE-TIME:20150319T090000Z DTEND;VALUE=DATE-TIME:20150319T103000Z DTSTAMP;VALUE=DATE-TIME:20150202T175926Z UID:840f844b-e1c8-442c-9a49-aa5aa7492f6a SEQUENCE:1 CREATED;VALUE=DATE-TIME:20150202T175926Z DESCRIPTION:Geography and Vertex NimG are both games played on a graph. On their turn\, a player moves a token along an arc and modifies the graph l ocally. In Geography\, the player removes the vertex the token was on or t he arc the token just slided along\, depending on the variant. In Vertex N imG\, the graph is weighted and the player decreases the weight of the ver tex the token was on or the weight of the vertex the token just arrived on \, depending of the variant. The game stops when a player cannot move. Und er the misère convention\, that player is considered the winner of the ga me. We see that these games are all pspace-hard in the general family of a ll graphs. LAST-MODIFIED;VALUE=DATE-TIME:20150402T224801Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/840f844b-e1c8-442c-9a49-aa5aa7492f6a END:VEVENT BEGIN:VEVENT SUMMARY:Didem Gözüpek\, «Equimatchable graphs are C_{2k+1}-free for k>= 4» DTSTART;VALUE=DATE-TIME:20151105T090000Z DTEND;VALUE=DATE-TIME:20151105T103000Z DTSTAMP;VALUE=DATE-TIME:20150914T142620Z UID:89bb2863-d28f-4059-b1b8-30d1638bec19 SEQUENCE:3 CREATED;VALUE=DATE-TIME:20150914T142620Z DESCRIPTION:A graph is equimatchable if all of its maximal matchings have the same size. Equimatchable graphs are extensively studied in the literat ure mainly from structural point of view. In this talk I will talk about\, to the best of our knowledge\, the fi rst family of forbidden subgraphs o f equimatchable graphs. Since equimatchable graphs are not hereditary by d efi nition\, this task of finding forbidden subgraphs requires the use of structural results from previous works. LAST-MODIFIED;VALUE=DATE-TIME:20151104T090103Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/89bb2863-d28f-4059-b1b8-30d1638bec19 END:VEVENT BEGIN:VEVENT SUMMARY:Dieter Rautenbach\, «Some pursuit-evasion games on graphs.» DTSTART;VALUE=DATE-TIME:20171005T080000Z DTEND;VALUE=DATE-TIME:20171005T090000Z DTSTAMP;VALUE=DATE-TIME:20170830T080657Z UID:b7b56441-7e8c-4df7-8f30-e02aa9135281 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20170830T080657Z DESCRIPTION:We consider variants of a pursuit and evasion game studied ind ependently by Britnell and Wildon as well as Haslegrave. In their game\, a cat has to catch an invisible mouse that moves along the edges of some gr aph $G$. In one of our versions\, the cat receives partial information abo ut its distance to the mouse\, and we show that the cat has a winning stra tegy if and only if $G$ is a forest. In a second version\, we study how we ll the cat can localize the mouse.\n\n\nThe results are joint work with Mo ritz Schneider and Dennis Dayanikli LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/b7b56441-7e8c-4df7-8f30-e02aa9135281 END:VEVENT BEGIN:VEVENT SUMMARY:Edouard Bonnet\, «Super-polynomial time approximability of inappr oximable problems» DTSTART;VALUE=DATE-TIME:20150423T090000Z DTEND;VALUE=DATE-TIME:20150423T100000Z DTSTAMP;VALUE=DATE-TIME:20150225T142018Z UID:b00dd530-d4c5-42fa-927a-b5e5bce80f82 SEQUENCE:5 CREATED;VALUE=DATE-TIME:20150225T142018Z DESCRIPTION:Most of the NP-hard problems are even hard to approximate with in some super-constant ratio (Max Clique\, Min Indepedent Dominating Set\, Min Set Cover etc.). For each of these problems\, from the known polytime $\\rho(n)$-approximation to the best super-polynomial time exact algorith m\, one can ask a continuum of question of the form: for $r < \\rho(n)$\, what is the best running time of an r-approximation algorithm? In 2013\, C halermsook\, Laekhanukit\, and Nanongkai answered the question for Max Ind ependent Set/Max Clique\, by showing that the previously known $r$-approxi mation in time $2^{n/r}$ was nearly optimal under standard complexity assu mptions. However\, for other problems there have been only some upper boun ds (by Bourgeois et al. and Cygan et al.) without nearly matching lower bo unds.\n\nWe start to fill this gap by showing that Min Independent Dominat ing Set\, Max Induced Path/Tree/Forest\, and Max Minimal Vertex Cover pres ent about the same behavior as Max Independent Set in being $\\rho(r)$-app roximable in time $2^{n/r}$ but not with a significantly better time. We a lso present some upper bounds for Min Asymmetric TSP and Max Grundy Colori ng. It is still unknown whether or not these two problems are polytime con stant-approximable. We conclude with some words concerning Min Set Cover.\ n\nThis is joint work with Michael Lampis and Vangelis Paschos. LAST-MODIFIED;VALUE=DATE-TIME:20150422T120102Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/b00dd530-d4c5-42fa-927a-b5e5bce80f82 END:VEVENT BEGIN:VEVENT SUMMARY:Dimitrios M. Thilikos\, «Bidimensionality Theory: a Retrospective » DTSTART;VALUE=DATE-TIME:20150903T080000Z DTEND;VALUE=DATE-TIME:20150903T093000Z DTSTAMP;VALUE=DATE-TIME:20150825T103924Z UID:5ff08751-39ec-42c4-997f-2e4d8e3721ce SEQUENCE:2 CREATED;VALUE=DATE-TIME:20150825T103924Z DESCRIPTION:We provide an exposition of the main results of the theory of bidimensionality in parameterized algorithm design. This theory applies to graph problems that are bidimensional in the sense that (i) their solutio n value is not increasing when we take minors or contractions of the inpu t graph and (ii) their solution value for the (triangulated) $(k\\times k )$-grid graph grows as a quadratic function of $k$. Under certain addition al conditions\, mainly of logical and combinatorial nature\, such problems admit sub-exponential parameterized algorithms and linear kernels when t heir inputs are restricted to certain topologically defined graph classes. We provide all formal definitions and concepts in order to present these results in a rigorous way and in their latest update. LAST-MODIFIED;VALUE=DATE-TIME:20150902T084314Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/5ff08751-39ec-42c4-997f-2e4d8e3721ce END:VEVENT BEGIN:VEVENT SUMMARY:Stéphane David-Grignot\, «Open-Membership Consensus Protocol» DTSTART;VALUE=DATE-TIME:20151001T080000Z DTEND;VALUE=DATE-TIME:20151001T093000Z DTSTAMP;VALUE=DATE-TIME:20150831T124144Z UID:ea71e76f-0389-408d-bdde-f1374baea20f SEQUENCE:1 CREATED;VALUE=DATE-TIME:20150831T124144Z DESCRIPTION:I will present David Mazières’ “Stellar Consensus Protoco l”\, a decentralized agreement process. Robustness from this approach to consensus\, stems from quorum slices\, individual trust decisions made by each node\, that together determine system-level quorums. This protocol i s a Byzantine agreement which makes no assumptions about the rational beha vior of attackers. Unlike prior Byzantine agreement models\, which presupp ose a unanimously accepted membership list\, this protocol enables any nod e to freely join and promotes organic network growth. Study perspectives w ill be outlined concerning the quorum slices function which makes an inter esting graph structure that is prone for an optimized implementation. A po tential application of the protocol as the base for a crypto-currency will also be introduced. LAST-MODIFIED;VALUE=DATE-TIME:20150930T080102Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/ea71e76f-0389-408d-bdde-f1374baea20f END:VEVENT BEGIN:VEVENT SUMMARY:Nicolas Bonichon\, «Upper and Lower Bounds for Competitive Online Routing on Delaunay Triangulations» DTSTART;VALUE=DATE-TIME:20150618T080000Z DTEND;VALUE=DATE-TIME:20150618T093000Z DTSTAMP;VALUE=DATE-TIME:20150527T150116Z UID:83590486-7392-49a2-b9f4-54e0d572f60f SEQUENCE:2 CREATED;VALUE=DATE-TIME:20150527T150116Z DESCRIPTION:Consider a weighted graph G where vertices are points in the p lane and edges are line segments. The weight of each edge is the Euclidean distance between its two endpoints. A routing algorithm on G has a compet itive ratio of c if the length of the path produced by the algorithm from any vertex s to any vertex t is at most c times the length of the shortest path from s to t in G. If the length of the path is at most c times the E uclidean distance from s to t\, we say that the routing algorithm on G has a routing ratio of c.We present an online routing algorithm on the Delaun ay triangulation with competitive and routing ratios of 5.90. This improve s upon the best known algorithm that has competitive and routing ratio 15. 48. The algorithm is a generalization of the deterministic 1-local routing algorithm by Chew on the L1-Delaunay triangulation. When a message follow s the routing path produced by our algorithm\, its header need only contai n the coordinates of s and t. This is an improvement over the currently kn own competitive routing algorithms on the Delaunay triangulation\, for whi ch the header of a message must additionally contain partial sums of dista nces along the routing path.We also show that the routing ratio of any det erministic k-local algorithm is at least 1.70 for the Delaunay triangulati on and 2.70 for the L1-Delaunay triangulation. In the case of the L1-Delau nay triangulation\, this implies that even though there exists a path betw een two points x and y whose length is at most 2.61|[xy]| (where |[xy]| de notes the length of the line segment [xy])\, it is not always possible to route a message along a path of length less than 2.70|[xy]|. From these bo unds on the routing ratio\, we derive lower bounds on the competitive rati o of 1.23 for Delaunay triangulations and 1.12 for L1-Delaunay triangulati ons.\n\nJoint work with Prosenjit Bose\, Jean-Lou De Carufel\, Ljubomir Pe rković\, and André Van Renssen. LAST-MODIFIED;VALUE=DATE-TIME:20150617T080103Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/83590486-7392-49a2-b9f4-54e0d572f60f END:VEVENT BEGIN:VEVENT SUMMARY:Isolde Adler\, «PAC learning of FO definable concepts & nowhere d ense graph classes» DTSTART;VALUE=DATE-TIME:20141009T080000Z DTEND;VALUE=DATE-TIME:20141009T093000Z DTSTAMP;VALUE=DATE-TIME:20140930T122045Z UID:5a5c5da2-c952-4654-8686-8b06dae1e036 SEQUENCE:0 CREATED;VALUE=DATE-TIME:20140930T122045Z DESCRIPTION:Let C be a graph class closed under subgraphs. We prove that a ll FO-definable concept classes on C allow example-efficient learnability (in the PAC model) if and only if C is nowhere dense. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:LIRMM\, E.3.23 URL:https://info-web.lirmm.fr/collorg/5a5c5da2-c952-4654-8686-8b06dae1e036 END:VEVENT BEGIN:VEVENT SUMMARY:Morgan Chopin\, «Complexité structurelle du problème du pompier » DTSTART;VALUE=DATE-TIME:20150430T080000Z DTEND;VALUE=DATE-TIME:20150430T093000Z DTSTAMP;VALUE=DATE-TIME:20150414T145307Z UID:722288d0-4ed6-49cb-b7c1-db236a8227e0 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20150414T145307Z DESCRIPTION:Dans cet exposé\, nous allons nous intéresser au problème d u pompier (firefighter) qui est défini de la manière suivante: initialem ent un sommet particulier d'un graphe non-orienté est brûlé. À chaque pas de temps\, on applique successivement les deux étapes suivantes: 1) P rotéger un sommet non-brûlé du graphe\, i.e. il ne peut plus brûler pa r la suite\; 2) Tous les sommets non-protégés et adjacents à un sommet brûlé sont brûlés. Le processus se termine lorsque plus aucun nouveau sommet ne peut brûler. Un sommet est alors considéré comme sauvé s'il n'est pas brûlé. L'objectif est de trouver une stratégie de protection telle que le nombre de sommets brûlés à la fin du processus est minimum . Nous considérons ici la version plus générale du problème qui permet de protéger b sommets par étape. Nous présenterons des résultats de c omplexité paramétrée de ce problème par rapport à des paramètres li és à la structure du graphe. En particulier\, nous montrerons que la com plexité du problème est directement liée à la largeur linéaire (pathw idth) et au degré maximum du graphe.\n\nRésultats obtenus en collaborati on avec Janka Chlebíková. LAST-MODIFIED;VALUE=DATE-TIME:20150429T080103Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/722288d0-4ed6-49cb-b7c1-db236a8227e0 END:VEVENT BEGIN:VEVENT SUMMARY:Éric Fusy\, «Bijections pour cartes d-angulées» DTSTART;VALUE=DATE-TIME:20150917T080000Z DTEND;VALUE=DATE-TIME:20150917T093000Z DTSTAMP;VALUE=DATE-TIME:20150728T210057Z UID:6faf1715-c993-4d52-8934-8e475f3b1bb0 SEQUENCE:2 CREATED;VALUE=DATE-TIME:20150728T210057Z DESCRIPTION:Nous présentons une méthode bijective générale pour les ca rtes planaires\, basée sur certaines orientations\, appliquée ici à deu x familles de cartes $d$-angulées pour $d \\geq 3$: les $d$-angulations d e maille $d$ (tous les cycles ont longueur au moins $d$)\, et les dissecti ons irréductibles $d$-angulées (où les seuls cycles de longueur $\\leq d$ sont les contours de faces internes). \n\nTravail en commun avec Oliv ier Bernardi. LAST-MODIFIED;VALUE=DATE-TIME:20150916T080103Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/6faf1715-c993-4d52-8934-8e475f3b1bb0 END:VEVENT BEGIN:VEVENT SUMMARY:Valia Mitsou\, «The computational complexity of two card games wi th theoretical applications» DTSTART;VALUE=DATE-TIME:20150507T080000Z DTEND;VALUE=DATE-TIME:20150507T093000Z DTSTAMP;VALUE=DATE-TIME:20150414T145138Z UID:b1e9fd4f-7f46-43f1-a037-b38376294397 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20150414T145138Z DESCRIPTION:The main theme of this talk is card games that can be naturall y reformulated as well-known graph-theoretic problems. In particular\, we will focus on two different games: the game of SET\, and the game of UNO. The objective of the former is to form sets of cards that match in a certa in sense\, while in the latter players need to discard their cards followi ng a matching rule (for more details regarding the rules of the two games please visit the following websites: official website of SET\, wikihow: ho w to play UNO). \n\nWe will describe connections of the two games with a n umber of different problems such as Multidimensional Matching\, Set Packin g\, Edge Dominating Set\, and Hamiltonian Path. These connections will hel p us show algorithmic as well as hardness results for variations of both g ames in the classical and the parameterized sense. The connections describ ed are two-fold as our results will\, in several cases\, imply progress fo r the state of the art of the corresponding graph-theoretic problems.\n\nT his talk will include results from two different publications: "The comput ational complexity of the game of SET"\, joint with Michael Lampis\, LATIN 2014\, and "Parameterized Edge Hamiltonicity"\, joint with Michael Lampis \, Kazuhisa Makino\, and Yushi UNO\, WG 2014. LAST-MODIFIED;VALUE=DATE-TIME:20150520T171134Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/b1e9fd4f-7f46-43f1-a037-b38376294397 END:VEVENT BEGIN:VEVENT SUMMARY:Pas de séminaire (JCALMs à Marseille)\, «TBA» DTSTART;VALUE=DATE-TIME:20151119T090000Z DTEND;VALUE=DATE-TIME:20151119T100000Z DTSTAMP;VALUE=DATE-TIME:20150924T074047Z UID:eb0f694f-f3e9-4d79-ba58-7a73d7bd6ed4 SEQUENCE:0 CREATED;VALUE=DATE-TIME:20150924T074047Z DESCRIPTION:TBA LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION: URL:https://info-web.lirmm.fr/collorg/eb0f694f-f3e9-4d79-ba58-7a73d7bd6ed4 END:VEVENT BEGIN:VEVENT SUMMARY:Dieter Rautenbach\, «Graphs in which some or every maximum matchi ng is uniquely restricted» DTSTART;VALUE=DATE-TIME:20151008T080000Z DTEND;VALUE=DATE-TIME:20151008T093000Z DTSTAMP;VALUE=DATE-TIME:20150903T094046Z UID:e9bd057b-03c5-4376-95d4-9198d681bc5c SEQUENCE:0 CREATED;VALUE=DATE-TIME:20150903T094046Z DESCRIPTION:A matching $M$ in a graph $G$ is uniquely restricted if there is no matching $M'$ in $G$ that is distinct from $M$ but covers the same v ertices as $M$. Solving a problem posed by Golumbic\, Hirst\, and Lewenste in\, we characterize the graphs in which some maximum matching is uniquely restricted. Solving a problem posed by Levit and Mandrescu\, we character ize the graphs in which every maximum matching is uniquely restricted. Bot h our characterizations lead to efficient recognition algorithms for the c orresponding graphs.\n\nJoint work with Lucia D. Penso and Uéverton dos S antos Souza. LAST-MODIFIED;VALUE=DATE-TIME:20151007T080103Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/e9bd057b-03c5-4376-95d4-9198d681bc5c END:VEVENT BEGIN:VEVENT SUMMARY:Marin Bougeret\, «On independent set on B1-EPG graphs» DTSTART;VALUE=DATE-TIME:20150910T080000Z DTEND;VALUE=DATE-TIME:20150910T093000Z DTSTAMP;VALUE=DATE-TIME:20150825T101608Z UID:bbe7f5a3-7b3b-4a9c-b6ab-b41f78a6fc29 SEQUENCE:2 CREATED;VALUE=DATE-TIME:20150825T101608Z DESCRIPTION:In this talk we consider the Maximum Independent Set problem ( MIS) on $B_1$-EPG graphs. EPG (for Edge intersection graphs of Paths on a Grid) is the class of graphs whose vertices can be represented as simple p aths on a rectangular grid so that two vertices are adjacent if and only i f the corresponding paths share at least one edge of the underlying grid. The restricted class $B_k$-EPG denotes EPG-graphs where every path has at most $k$ bends. It was already known that MIS on $B_1$-EPG graphs is NP-co mplete and admits a $4$-approximation.\n\nIn this talk we consider the app roximability and the fixed parameter tractability of MIS on $B_1$-EPG. We will discuss the conditions guaranteeing the existence of a PTAS\, and we will show that MIS is FPT in the standard parameterization on $B_1$-EPG r estricted to only three shapes of path. As we know that MIS is W1-hard on $B_2$-EPG\, the main open question is the FPT status on general $B_1$-EPG. \n\nTravail en commun avec Stéphane Bessy\, Daniel Gonçalves et Christop he Paul. LAST-MODIFIED;VALUE=DATE-TIME:20150909T140258Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/bbe7f5a3-7b3b-4a9c-b6ab-b41f78a6fc29 END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Gonçalves\, «Planar graphs as L-intersection or L-contact graphs» DTSTART;VALUE=DATE-TIME:20171019T080000Z DTEND;VALUE=DATE-TIME:20171019T090000Z DTSTAMP;VALUE=DATE-TIME:20171016T124912Z UID:5ab0c698-eb6e-4174-9079-7b54ce46174d SEQUENCE:0 CREATED;VALUE=DATE-TIME:20171016T124912Z DESCRIPTION:En collaboration avec Lucas Isenmann et Claire Pennarun\n\nThe L-intersection graphs are the graphs that have a representation as inters ection graphs of axis parallel shapes in the plane. A subfamily of these g raphs are {L\, |\, -}-contact graphs which are the contact graphs of axis parallel L\, |\, and - shapes in the plane. We prove here two results that were conjectured by Chaplick and Ueckerdt in 2013. We show that planar gr aphs are L-intersection graphs\, and that triangle-free planar graphs are {L\, |\, -}-contact graphs. These results are obtained by a new and simple decomposition technique for 4-connected triangulations. Our results also provide a much simpler proof of the known fact that planar graphs are segm ent intersection graphs. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/5ab0c698-eb6e-4174-9079-7b54ce46174d END:VEVENT BEGIN:VEVENT SUMMARY:François Dross\, «Décomposition fractionnelle en triangles de g raphes presque complets» DTSTART;VALUE=DATE-TIME:20150924T080000Z DTEND;VALUE=DATE-TIME:20150924T093000Z DTSTAMP;VALUE=DATE-TIME:20150911T105624Z UID:5a6e657f-1580-4696-9356-06b1e53370fb SEQUENCE:1 CREATED;VALUE=DATE-TIME:20150911T105624Z DESCRIPTION:Une décomposition (entière) d'un graphe en triangles est une partition de ses arêtes en triangles. Une décomposition fractionnelle d 'un graphe en triangles est une assignation d'un poids positif à chaque t riangle du graphe tel que\, pour toute arête e\, la somme des poids des t riangles contenant e est égale à 1. On montre que tout graphe à n somme ts de degré minimum au moins 0.9n a une décomposition fractionnelle en t riangles.\n\nLa preuve se fait en partant d'une affectation simple de poid s aux triangles\, et en l'adaptant pour obtenir une décomposition fractio nnelle en triangles. LAST-MODIFIED;VALUE=DATE-TIME:20150923T080103Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/5a6e657f-1580-4696-9356-06b1e53370fb END:VEVENT BEGIN:VEVENT SUMMARY:Andreas Schmid\, «A New Approach for the Maximum Planar Subgraph Problem» DTSTART;VALUE=DATE-TIME:20200109T090000Z DTEND;VALUE=DATE-TIME:20200109T100000Z DTSTAMP;VALUE=DATE-TIME:20191212T090654Z UID:27b2656a-5eb1-4d64-90d4-68f2e1554824 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20191212T090654Z DESCRIPTION:A cactus graph is a graph in which any two cycles are edge-dis joint. We present a constructive proof of the fact that any plane graph G contains a cactus subgraph C where C contains at least a 1/6 fraction of t he triangular faces of G. We also show that this ratio cannot be improved by showing a tight lower bound. Together with an algorithm for linear matr oid parity\, our bound implies two approximation algorithms for computing "dense planar structures" inside any graph:\n\n(i) A 1/6 approximation alg orithm for\, given any graph G\, finding a planar subgraph with a maximum number of triangular faces\; this improves upon the previous 1/11-approxim ation\;\n\n(ii) An alternate (and arguably more illustrative) proof of the 4/9 approximation algorithm for finding a planar subgraph with a maximum number of edges.\n\nOur bound is obtained by analyzing a natural local sea rch strategy and heavily exploiting the exchange arguments. Therefore\, th is suggests the power of local search in handling problems of this kind. LAST-MODIFIED;VALUE=DATE-TIME:20200108T090104Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/27b2656a-5eb1-4d64-90d4-68f2e1554824 END:VEVENT BEGIN:VEVENT SUMMARY:Florian Barbero\, «Parameterized and Optimization algorithm for t he c-Load Coloring problem» DTSTART;VALUE=DATE-TIME:20151126T090000Z DTEND;VALUE=DATE-TIME:20151126T103000Z DTSTAMP;VALUE=DATE-TIME:20150914T150918Z UID:6c0534aa-228e-4145-bb9e-ca617c73787f SEQUENCE:3 CREATED;VALUE=DATE-TIME:20150914T150918Z DESCRIPTION:For a positive integer $c$\, let $[c] = \\{1\, \\ldots \, c\\} $. The $c$-Load Coloring problem is as follows: given a graph $G=(V\,E)$ a nd an integer $k$ as parameter\, decide whether there exists a coloring $q : V \\to [c]$ such that for every $i$ in $[c]$\, there are $k$ edges with both endvertices colored $i$ in $q$.\n\nThis problem was studied when $c = 2$ inter alia for its application in broadcast WDM communication network s. It was known that 2-Load Coloring is NP-complete and has a constant rat io approximation. For this sub-case\, we had a kernel with at most $7k$ ve rtices and a dynamic programming algorithm simple-exponential in treewidth \, thus 2-Load Coloring is FPT simple-exponential.\n\nDuring my internship in Royal Holloway\, I generalized and improved all these results by obtai ning a linear-vertex and linear-edge kernel for c-Load Coloring\, $c > 1$ being fixed. To prove this kernel\, I described a new obstacle I called ov erload\, and showed how to use the related reduction rules in polynomial t ime. These results imply that $c$-Load Coloring is FPT simple-exponential and the optimization version of $c$-Load Coloring (where $k$ is to be maxi mized) has an approximation algorithm with a constant ratio. It is even po ssible that this problem admits a sub-exponential parametrized algorithm. I proved this complexity for graphs of bounded genus\, chordal graphs and $H$-free families\, where $H$ is a constant forbidden minor. The team of m y internship supervisor and I published a conference paper in the Internat ional Symposium on Parameterized and Exact Computation (IPEC 2015). LAST-MODIFIED;VALUE=DATE-TIME:20151125T090105Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/6c0534aa-228e-4145-bb9e-ca617c73787f END:VEVENT BEGIN:VEVENT SUMMARY:Spencer Backman\, «Graph Fourientations and the Tutte Polynomial » DTSTART;VALUE=DATE-TIME:20151112T090000Z DTEND;VALUE=DATE-TIME:20151112T103000Z DTSTAMP;VALUE=DATE-TIME:20150914T142451Z UID:4cdd8084-99da-4bb7-97bf-0e5278887de3 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20150914T142451Z DESCRIPTION:A fourientation of a graph is a choice for each edge whether t o orient that edge in either direction\, leave it unoriented\, or biorient it. Fourientations can naturally be viewed as a mixture of graph orienta tions and subgraphs where unoriented and bioriented edges play the roles o f absent and present edges\, respectively. The Tutte polynomial is the mo st general bivariate polynomial associated to a graph which can be defined using the deletion and contraction of edges. I will describe joint work with Sam Hopkins where we investigate properties of cuts and cycles in fou rientations which determine classes of fourientations which are enumerated by Tutte polynomial evaluations. Time permitting\, I will illustrate how several of these classes relate to algebraic\, combinatorial\, and geomet ric topics such as Riemann-Roch theory for graphs\, bigraphical arrangemen ts\, Lawrence ideals\, zonotopal algebras\, and the reliability polynomial . LAST-MODIFIED;VALUE=DATE-TIME:20151111T090105Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/4cdd8084-99da-4bb7-97bf-0e5278887de3 END:VEVENT BEGIN:VEVENT SUMMARY:Marin Bougeret\, «Triangle packing in (sparse) tournaments: appro ximation and kernelization.» DTSTART;VALUE=DATE-TIME:20171109T090000Z DTEND;VALUE=DATE-TIME:20171109T100000Z DTSTAMP;VALUE=DATE-TIME:20171025T131920Z UID:15ef9679-0699-4f2a-bfd2-304f2b96c1c7 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20171025T131920Z DESCRIPTION:Given a tournament T and a positive integer k\, the C_3-Packin g-T asks if there exists a least k (vertex-)disjoint directed 3-cycles in T. This is the dual problem in tournaments of the classical minimal feedba ck vertex set problem. Surprisingly C_3-Packing-T did not receive a lot of attention in the literature. We show that it does not admit a PTAS unless P=NP\, even if we restrict the considered instances to sparse tournaments \, that is tournaments with a feedback arc set (FAS) being a matching. Foc using on sparse tournaments we provide a (1+6/(c-1)) approximation algorit hm for sparse tournaments having a linear representation where all the bac kward arcs have “length” at least c. Concerning kernelization\, we sho w that C_3-Packing-T admits a kernel with O(m) vertices\, where m is the s ize of a given feedback arc set. In particular\, we derive a O(k) vertices kernel for C_3-Packing-T when restricted to sparse instances. On the nega tive size\, we show that C_3-Packing-T does not admit a kernel of (total b it) size O(k^{2-epsilon}) unless NP is a subset of coNP / Poly. The existe nce of a kernel in O(k) vertices for C_3-Packing-T remains an open questio n.\n\nJoint work with Stéphane Bessy and Jocelyn Thiebaut. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/15ef9679-0699-4f2a-bfd2-304f2b96c1c7 END:VEVENT BEGIN:VEVENT SUMMARY:Dimitrios Thilikos\, «Hitting Topological Minor Models in Planar Graphs is Fixed Parameter Tractable» DTSTART;VALUE=DATE-TIME:20191212T090000Z DTEND;VALUE=DATE-TIME:20191212T100000Z DTSTAMP;VALUE=DATE-TIME:20191203T141846Z UID:c69dd6e8-2d77-46bb-8cc1-c210e0f60552 SEQUENCE:0 CREATED;VALUE=DATE-TIME:20191203T141846Z DESCRIPTION:For a finite collection of graphs ${\\cal F}$\, the ${\\cal F} $-TM-Deletion problem has as input an $n$-vertex \ngraph $G$ and an intege r $k$ and asks whether there exists a set $S \\subseteq V(G)$ with $|S| \ \leq k$ such that $G \\setminus S$ does not contain any of the graphs in $ {\\cal F}$ as a topological minor. We prove that for every such ${\\cal F} $\, ${\\cal F}$-TM-Deletion\nis fixed parameter tractable on planar graphs . In particular\, we provide an $f(h\,k)\\cdot n^{2}$ algorithm where $h$ is an upper bound to the vertices of the graphs in ${\\cal F}$.\n\nJoint work with Petr A. Golovach and Giannos Stamoulis LAST-MODIFIED;VALUE=DATE-TIME:20191211T090103Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/c69dd6e8-2d77-46bb-8cc1-c210e0f60552 END:VEVENT BEGIN:VEVENT SUMMARY:Ilkyoo Choi\, «Obtaining chi-bounded families by forbidding subst ructures» DTSTART;VALUE=DATE-TIME:20151203T090000Z DTEND;VALUE=DATE-TIME:20151203T101500Z DTSTAMP;VALUE=DATE-TIME:20151126T101829Z UID:26de1823-2845-491b-a27e-55744658b201 SEQUENCE:2 CREATED;VALUE=DATE-TIME:20151126T101829Z DESCRIPTION:The clique number is a trivial lower bound for the chromatic n umber of a graph. Since Erd\\H{o}s showed the existence of graphs with arb itrarily high chromatic number and arbitrarily high girth (so clique numbe r is 2)\, in general\, the chromatic number of a graph cannot be upper bou nded by a function of its clique number. A class of graphs is said to be $ \\chi$-bounded if such a function exists.\n\nVertex-minor and pivot-minors are graph containment properties such as (induced) subgraphs\, subdivisio ns\, and minors. Geelen conjectured that for any fixed graph $H$\, the cla ss of graphs with no $H$-vertex-minor is $\\chi$-bounded. This conjecture was known to be true only for one graph (proved by Dvo\\v{r}\\'ak and Kr\\ 'al)\, but recently Chudnovsky\, Scott\, and Seymour proved it for any cyc le. We add another class of graphs for which Geelen's Conjecture is true\, namely\, fan graphs.\n\nWe also ask the following question of whether Gee len's Conjecture can be generalized to pivot-minors: for any fixed graph $ H$\, are the class of graphs with no $H$-pivot-minor $\\chi$-bounded? We g ive some positive evidence to this question by proving that it is true for all cycles\, which is a strengthening of the aforementioned result by Chu dnovsky\, Scott\, and Seymour. This result can also be viewed as a partial result of the last open conjecture among the three conjectures made by Gy \\'arf\\'as' in 1985. LAST-MODIFIED;VALUE=DATE-TIME:20151202T090102Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/26de1823-2845-491b-a27e-55744658b201 END:VEVENT BEGIN:VEVENT SUMMARY:Alan Diego Aurélio Carneiro\, «Complexity Analysis of Deadlock R esolution Graph Problems.» DTSTART;VALUE=DATE-TIME:20181129T090000Z DTEND;VALUE=DATE-TIME:20181129T100000Z DTSTAMP;VALUE=DATE-TIME:20181107T214122Z UID:513f132b-cc9f-4110-ac3b-76c0c7a8222e SEQUENCE:1 CREATED;VALUE=DATE-TIME:20181107T214122Z DESCRIPTION:A deadlock occurs in a distributed computation if a group of p rocesses wait indefinitely for resources from each other. We study actions to be taken after deadlock detection\, especially the action of searching for a small deadlock-resolution set. More precisely\, given a “snapshot ” graph G representing a deadlocked state of a distributed computation g overned by a certain deadlock model M\, we investigate the complexity of v ertex/arc deletion problems that aim at finding minimum vertex/arc subsets whose removal turns G into a deadlock-free graph (according to model M). We present a computational complexity mapping considering the particular c ombination of deletion operations and deadlock models. A special attention is given to Vertex–Deletion(OR)\, which consists of determining whether G has a subset S ⊆ V(G) of size at most k such that G[V∖S] contains n o knot. A knot in a directed graph G is a strongly connected subgraph Q of G with size at least two\, such that no vertex in V(Q) is an in-neighbor of a vertex in V(G)∖V(Q). Our main contributions is a parameterized comp lexity analysis of the Vertex–Deletion(OR) problem. Vertex–Deletion(OR ) is a graph problem with natural applications in deadlock resolution\, an d it is closely related to Directed Feedback Vertex Set. We prove that: Ve rtex–Deletion(OR) is W[1]-hard when parameterized by the size of the sol ution\; it can be solved in time\, but assuming SETH it cannot be solved i n time\, where φ is the size of the largest strongly connected subgraph o f G\; it can be solved in time\, but assuming ETH it cannot be solved in t ime\, where Ф is the number of vertices with out-degree at most k\; unles s \, Vertex–Deletion(OR) does not admit polynomial kernel even when φ=2 and k is the parameter.\n\nAuthors : Alan Carneiro\, Fábio Protti and U éverton Souza. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/513f132b-cc9f-4110-ac3b-76c0c7a8222e END:VEVENT BEGIN:VEVENT SUMMARY:Dimitrios M. Thilikos\, «Optimal Erdős-Pósa for pumpkins: verte x and edge variants and approximation algorithms» DTSTART;VALUE=DATE-TIME:20140904T080000Z DTEND;VALUE=DATE-TIME:20140904T090000Z DTSTAMP;VALUE=DATE-TIME:20150201T015032Z UID:14eaf79b-348f-4d5b-a01a-17b1f19c0f80 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20150201T015032Z DESCRIPTION:The origin of the study of Erdős-Pósa properties comes from the celebrated Erdős-Pósa Theorem (1965)\, stating that there is a natur al function $f$ such that for every positive integer $k$ and for every gra ph $G$\, either $G$ contains $k$ vertex-disjoint cycles or there is a set $X$ of $f(k)$ vertices in $G$ meeting all cycles of $G$. In particular\, E rdős and Pósa proved this result for $f(k)=O(k\\cdot \\log k)$ and showe d that this bound is optimal. Given a graph $J$\, we denote by ${\\cal M}( J)$ the set of all graphs that can be contracted to $J$ (also called //mod els// of $J$). Robertson and Seymour proved that the class ${\\cal M}(J)$ satisfies the Erdős-Pósa property if and only if $J$ is planar. Notice t hat this can be seen as a major extension of the Erdős-Pósa Theorem (tak e $J=\\theta_{2}$ where\, in general\, $\\theta_{r}$ is the graph consisti ng of two vertices and $r$ parallel edges between them). The emerging ques tion is whether (and when) the function involved in the above proposition can match the (optimal) $O(k\\cdot \\log k)$ bound of Erdős-Pósa and whe ther this bound can be improved under several assumptions on the graphs it applies. Given two graphs $H$ and $G$\, we denote by ${\\bf pack}^{\\sf v }_{H}(G)$ (resp. ${\\bf pack}^{\\sf e}_{H}(G)$) the maximum number of vert ex (resp. edge)-disjoint models of $H$ in $G$. We also denote by ${\\bf co ver}^{\\sf v}_{H}(G)$ resp. ${\\bf cover}^{\\sf v}_{H}(G)$) the minimum nu mber of vertices (resp. edges) that intersect all models of $H$ in $G$.\n\ nWe give a unified proof of the following result.\n\nTheorem: For every ${ \\sf x}\\in\\{{\\sf v}\,\n{\\sf e}\\}$\, there exists a function $f:\\Bbb{ N}\\rightarrow\\Bbb{N}$ such that for every two positive integers $r\,q$ a nd every graph $G$ excluding $K_{q}$ as a minor\, it holds that ${\\bf cov er}^{\\sf x}_{\\theta_{r}}(G)\\leq f(r)\\cdot {\\bf pack}^{\\sf x}_{\\thet a_{r}}(G)\\cdot \\log q$.\n\nOur results also imply that\, for every ${\\s f x}\\in\\{{\\sf v}\,\n{\\sf e}\\}$ and $r$\, the problems of computing th e values of ${\\bf pack}^{\\sf x}_{\\theta_{r}}$ and ${\\bf cover}^{\\sf x }_{\\theta_{r}}$\, admit $\\log(OPT)$-approximation (deterministic and pol ynomial) algorithms. This improves existing results on the approximability for the case where ${\\sf x}={\\sf v}$.\n\n(Joint work with: Dimitris Cha tzidimitriou\, Jean-Florent Raymond\, and Ignasi Sau). LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/14eaf79b-348f-4d5b-a01a-17b1f19c0f80 END:VEVENT BEGIN:VEVENT SUMMARY:Pascal Ochem\, «Partitioning into disjoint cliques and a triangle -free graph» DTSTART;VALUE=DATE-TIME:20160121T090000Z DTEND;VALUE=DATE-TIME:20160121T103000Z DTSTAMP;VALUE=DATE-TIME:20160106T110857Z UID:45acb32e-931d-4003-9ce9-06496aa98783 SEQUENCE:8 CREATED;VALUE=DATE-TIME:20160106T110857Z DESCRIPTION:We consider the complexity of deciding whether a graph admits a vertex partition into two parts R and B such that R is K_3-free and B is P_3-free. We show that the problem is NP-complete for 9 small graph class es\, where "small" means that if we take the intersection of any two class es among these nine\, the problem becomes trivial because the answer is al ways yes.\n\nJoint work with Marin Bougeret. LAST-MODIFIED;VALUE=DATE-TIME:20160120T090103Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/45acb32e-931d-4003-9ce9-06496aa98783 END:VEVENT BEGIN:VEVENT SUMMARY:pas de séminaire (cours Petr Golovach)\, «TBA» DTSTART;VALUE=DATE-TIME:20170914T080000Z DTEND;VALUE=DATE-TIME:20170914T080000Z DTSTAMP;VALUE=DATE-TIME:20170912T080915Z UID:61b7b193-9649-410e-91ed-9c9394246834 SEQUENCE:0 CREATED;VALUE=DATE-TIME:20170912T080915Z DESCRIPTION:TBA LAST-MODIFIED;VALUE=DATE-TIME:20170912T081605Z LOCATION: URL:https://info-web.lirmm.fr/collorg/61b7b193-9649-410e-91ed-9c9394246834 END:VEVENT BEGIN:VEVENT SUMMARY:Jean-Florent Raymond\, «Mineurs de cliques dans les graphes de gr ande maille» DTSTART;VALUE=DATE-TIME:20151217T090000Z DTEND;VALUE=DATE-TIME:20151217T103000Z DTSTAMP;VALUE=DATE-TIME:20151130T174314Z UID:4486245b-4575-4a06-b72c-b6a628fde386 SEQUENCE:3 CREATED;VALUE=DATE-TIME:20151130T174314Z DESCRIPTION:En 2003\, Kühn et Osthus ont prouvé que tout graphe sans pet it sommet contient comme mineur une clique de taille exponentiellement gra nde par rapport à sa maille (càd la taille d'un plus petit cycle).\n \nE n étendant la notion de maille\, nous donnons des conditions alternatives pour qu'un graphe contienne une grande clique comme mineur. Pour tout gra phe H\, la H-maille d'un graphe G et la taille d'un plus petit sous-graphe de G qui se contracte en H. Cette notion généralise celle de maille qui correspond à la θ_2-maille\, où θ_r est le graphe à 2 sommets et r a rêtes.\n\nNous montrons que pour tout entier r\, les graphes de grand deg ré minimum contiennent comme mineur des cliques dont l'ordre est une fonc tion exponentielle de leur θ_r-maille. Ce résultat étend celui de Kühn et Osthus à la notion de H-maille. Nous donnons également des critères de connectivité garantissant la présence d'une telle clique.\n\nCes ré sultats peuvent être utilisés par exemple pour obtenir des théorèmes d e type Erdős-Pósa\, ou pour borner la tree-width des graphes excluant ce rtains mineurs.\n\nTravail commun avec Dimitris Chatzidimitriou (National and Kapodistrian University of Athens)\, Ignasi Sau (LIRMM) et Dimitrios M . Thilikos (LIRMM et National and Kapodistrian University of Athens). LAST-MODIFIED;VALUE=DATE-TIME:20151216T090104Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/4486245b-4575-4a06-b72c-b6a628fde386 END:VEVENT BEGIN:VEVENT SUMMARY:Aurelie Lagoutte\, «Coloring perfect graphs with bounded clique n umber» DTSTART;VALUE=DATE-TIME:20160128T090000Z DTEND;VALUE=DATE-TIME:20160128T103000Z DTSTAMP;VALUE=DATE-TIME:20160104T073403Z UID:27dea7cd-f871-4d21-abe9-814879ce1371 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20160104T073403Z DESCRIPTION:Perfect graphs are graphs for which the chromatic number match es the trivial lower bound consisting in the clique number (and the same h olds for every induced subgraph). After the long study that led to the Str ong Perfect Graph Theorem\, the main open question concerning them is abou t finding an optimal coloring with a combinatorial algorithm.\nIndeed\, de ciding if the chromatic number of a graph is at most k is NP-complete in g eneral\, and even if k=3. A famous result of Lovasz\, Grötchel and Schrij ver provides a polynomial-time algorithm that optimally colors any perfect graph\, however this algorithm uses the ellipsoid method which makes it unpractical and not combinatorial.\nWe design a purely combinatorial algor ithm that\, given in input a perfect graph\, outputs an optimal coloring i n time O(n^f) where f is quadratic in the clique number omega(G).\n\nThis is joint work with Maria Chudnovsky\, Paul Seymour and Sophie Spirkl. LAST-MODIFIED;VALUE=DATE-TIME:20160128T143629Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/27dea7cd-f871-4d21-abe9-814879ce1371 END:VEVENT BEGIN:VEVENT SUMMARY:pas de séminaire (25 ans du Lirmm)\, «TBA» DTSTART;VALUE=DATE-TIME:20170928T080000Z DTEND;VALUE=DATE-TIME:20170928T080000Z DTSTAMP;VALUE=DATE-TIME:20170912T081045Z UID:40ba324e-6ce9-4158-92ff-9554e35eb1d3 SEQUENCE:0 CREATED;VALUE=DATE-TIME:20170912T081045Z DESCRIPTION:TBA LAST-MODIFIED;VALUE=DATE-TIME:20170912T081605Z LOCATION: URL:https://info-web.lirmm.fr/collorg/40ba324e-6ce9-4158-92ff-9554e35eb1d3 END:VEVENT BEGIN:VEVENT SUMMARY:Mark Jones\, «Parameterized Complexity of the Mixed Chinese Postm an Problem» DTSTART;VALUE=DATE-TIME:20160107T090000Z DTEND;VALUE=DATE-TIME:20160107T103000Z DTSTAMP;VALUE=DATE-TIME:20151201T111803Z UID:a5c1d508-9a50-47fa-a07e-737a262c29ae SEQUENCE:3 CREATED;VALUE=DATE-TIME:20151201T111803Z DESCRIPTION:In the Mixed Chinese Postman Problem (MCPP)\, given an edge-we ighted mixed graph G (G may have both edges and arcs)\, our aim is to find a minimum weight closed walk traversing each edge and arc at least once. The MCPP was known to be polynomial-time solveable on graphs containing on ly edges or only arcs. It was known to be fixed-parameter tractable parame terized by the number of edges using a simple argument. In this talk\, I'l l show that the MCPP parameterized by the number of arcs is also fixed-par ameter tractable. The proof uses a well-known result of Marx\, O'Sullivan and Razgon on the treewidth of torso graphs with respect to small separato rs. We obtain a small cut analog of this result\, and use it to construct a tree decomposition which\, despite not having bounded width\, has other properties allowing us to design a fixed-parameter algorithm. I will also discuss structural parameterizations of the MCPP\, including treewidth and treedepth. LAST-MODIFIED;VALUE=DATE-TIME:20160106T090102Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/a5c1d508-9a50-47fa-a07e-737a262c29ae END:VEVENT BEGIN:VEVENT SUMMARY:Emeric Gioan\, «A Survey on The Active Bijection in Graphs\, Hype rplane Arrangements\, and Oriented Matroids» DTSTART;VALUE=DATE-TIME:20160114T090000Z DTEND;VALUE=DATE-TIME:20160114T103000Z DTSTAMP;VALUE=DATE-TIME:20151102T163650Z UID:460c97ab-6568-4b6c-82fe-7e3be7251186 SEQUENCE:7 CREATED;VALUE=DATE-TIME:20151102T163650Z DESCRIPTION:En preambule de l'abstract general\, je previens qu'il s'agira d'un expose assez vaste et plus long que d'habitude (1h30)\, et qu'il y a ura deux brefs passage type groupe de travail pour poser les questions sui vantes aux algorithmiciens de l'equipe\, propices pour approfondissements dans le cas particulier des graphes (cf. details dans courriel et article envoyes a l'equipe en octobre) :\n\n1 - On s'interesse aux graphes bipolai res et on en definit une coupe optimale. Combien coute de trouver une coup e orientee de poids minimum\, pour une fonction poids sur les aretes posit ive ou nulle ? Combien coute de trouver une coupe de poids minimum\, orien tee sauf pour certaines aretes d'un arbre couvrant\, pour un poids qui est positif/negatif selon l'orientation de ces aretes ? (je sais repondre pol ynomialement mais en passant par la programmation lineaire\, j'aimerais de s solutions en termes de graphes)\n\n2 - On introduit une decomposition de s graphes orientes en graphes bipolaires (cycliques ou acycliques) dont le s nombres sont des parametres combinatoires classiques. Cela pourrait-il e tre utilise en complexite parametree ? Verriez-vous par exemple un problem e facile sur les graphes bipolaires\, et resoluble en decomposant un graph e acyclique (ou fortement connexe) en de tels mineurs ?\n\n\n------------- ------------------------------------------\n\nThe active bijection maps an y directed graph\, resp. signed hyperplane arrangement or oriented matroid \, defined on a linearly ordered edge set\, resp. ground set\, onto one of its spanning trees\, resp. bases.\n\nIt relates all spanning trees to all orientations of a graph\, all bases to all reorientations of an hyperplan e arrangement or\, more generally\, an oriented matroid. It preserves acti vities: for bases in the sense of Tutte\, for orientations in the sense of Las Vergnas\, yielding a bijective interpretation of the equality of two expressions of the Tutte polynomial. It preserves also some active partiti ons associated with orientations and bases. It can be mathematically defin ed in a short way\, and can be built\, characterized\, particularized\, or refined in several ways.\n\nNotably\, we get a bijection between bounded regions (bipolar orientations in the case of a graph) and bases with inter nal activity one and external activity zero\, which can be seen as an adva nced refinement of real (pseudo)linear programming. We get a bijection bet ween classes of reorientations and bases\, using a decomposition into boun ded regions of minors of the primal and the dual\, which also has a counte rpart for decomposing matroid bases\, and yields an expression of the Tutt e polynomial using only beta invariants of minors.\n\nWe also get activity preserving bijections between all reorientations and all subsets (related to a four-variable expression of the Tutte polynomial)\, between regions and no-broken-circuit subsets (acyclic case)\, between reorientations with fixed orientations for smallest elements of positive circuits/cocircuits (directed cycles/cocycles) and bases (spanning trees)\, between increasing trees and permutations (complete graph case)\, etcetera.\n\nIt is the sub ject of a series of papers\, joint with Michel Las Vergnas. LAST-MODIFIED;VALUE=DATE-TIME:20160113T090103Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/460c97ab-6568-4b6c-82fe-7e3be7251186 END:VEVENT BEGIN:VEVENT SUMMARY:Ararat Harutyunyan\, «A proof of a conjecture of Barat and Thomas sen» DTSTART;VALUE=DATE-TIME:20160218T090000Z DTEND;VALUE=DATE-TIME:20160218T103000Z DTSTAMP;VALUE=DATE-TIME:20160108T133405Z UID:4d4a6292-4169-463e-8fdf-386a4e7c7bab SEQUENCE:1 CREATED;VALUE=DATE-TIME:20160108T133405Z DESCRIPTION:The Barat-Thomassen conjecture asserts that for every tree T o n m edges\, there exists a constant k such that every k-edge-connected gra ph with size divisible by m can be edge-partitioned into copies of T . The conjecture has been verified when T is a path or when T has diameter at m ost 4. In the talk\, I will sketch a recent proof of the conjecture. \n\nT his is joint work with J. Bensmail\, T.-N. Le\, M. Merker and S. Thomassé . LAST-MODIFIED;VALUE=DATE-TIME:20160217T090104Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/4d4a6292-4169-463e-8fdf-386a4e7c7bab END:VEVENT BEGIN:VEVENT SUMMARY:Florian Barbero\, «Cutwidth in Semi-Complete Digraphs» DTSTART;VALUE=DATE-TIME:20160211T090000Z DTEND;VALUE=DATE-TIME:20160211T103000Z DTSTAMP;VALUE=DATE-TIME:20160119T191610Z UID:f90d6688-4d93-45b0-982d-cf46ec5411fc SEQUENCE:1 CREATED;VALUE=DATE-TIME:20160119T191610Z DESCRIPTION:(English Below)\n\nEn collaboration avec Michal Pilipczuk (MIM UW\, Warsaw).\n\nUn digraphe $D = (V\,E)$ est dit \\emph{semi-complet} s'i l est simple (pas de self-loop\, pas de multi-edge) et que pour tous somme ts $u\,v \\in V$ différents\, l'arc $(u\,v)$ ou l'arc $(v\,u)$ est prése nt dans $E$. De plus\, $D$ est un \\emph{tournoi} si pour tous sommets $u\ ,v \\in V$ différents $(u\,v)$ et $(v\,u)$ ne sont pas simultanément pr ésents. Récemment\, Chudnovsky\, Fradkin et Seymour ont montré que la r elation d'immersion restrainte aux digraphes semi-complets était WQO en u tilisant la mesure de largeur associée\, appellée \\emph{Cutwidth}. Ces notions ont ainsi trouvé un regain d'intérêt.\n\nDurant ce séminaire\, nous nous intéresserons à la cutwidth\, définie de la manière suivant e. Etant donné un digraphe $D$\, un ordre $\\pi$ sur les sommets de $D$ e t une position $i \\in [n]$\, la $i$-ème coupe selon $\\pi$ de $D$ est l' ensemble d'arcs de retour $D(\\pi\,i) = \\{(v\,u) \\in E : u \\in \\pi[i]\ , v \\in V \\setminus \\pi[i]$\, avec $\\pi[i]$ représentant les $i$ prem iers sommets de $\\pi$. La cutwidth de $\\pi$ est $ctw(D\,\\pi) = \\max_{i \\in [n]} D(\\pi\,i)$ et la cutwidth de $D$ est $ctw(D) = \\min_{\\pi} ct w(D\,\\pi)$.\n\nComme pour de nombreuses mesures de largeur\, calculer la cutwidth est NP-Difficile dans le cas général. Nous prouverons que cela reste vrai lorsqu'on se restreint aux semi-complets mais qu'il est possibl e de calculer la cutwidth d'un tournoi en temps polynomial. A partir de ce s résultats\, nous montrerons comment approximer la cutwidth d'un semi-co mplet (de façon non linéaire toutefois) ou comment construire des petits tournois de cutwidth donnée. Nous montrerons aussi que tout tournoi cont ient un sous-tournoi induit de même cutwidth $c$ et de taille au plus lin éaire en $c$. Nous étudierons également des variantes de {\\sc Feedback Vertex/Edge Deletion}\, à savoir {\\sc Cutwidth Vertex Deletion} et {\\s c Cutwidth Arc Reversal} (dans le cas restreint des semi-complets).\n\n--\ nWith Michal Pilipczuk (MIMUW\, Warsaw).\n\nA digraph $D = (V\,E)$ is \\em ph{semi-complete} if it is simple (no self-loop\, no multi-edge)\, and tha t\, for all different vertices $u\,v \\in V$\, the arc $(u\,v)$or the arc $(v\,u)$ is present in $E$. Moreover\, $D$ is a \\emph{tournament} if for all different vertices $u\,v \\in V$\, $(u\,v)$ and $(v\,u)$ cannot be sim ultaneously present. Recently\, Chudnovsky\, Fradkin and Seymour proved th at the immersion relation restricted to semi-complete digraphs is WQO\, us ing the associated width measure called \\emph{Cutwidth}. Hence\, these no tions deserve to be studied.\n\nDuring this seminar\, we will focus on cut width\, defined as follows. Given a digraph $D$\, an ordering $\\pi$ of th e vertices of $D$ and a position $i \\in [n]$\, the cut at position $i$ of $D$ using $\\pi$ is the set of feedback arcs $D(\\pi\,i) = \\{(v\,u) \\in E : u \\in \\pi[i]\, v \\in V \\setminus \\pi[i]$\, with $\\pi[i]$ being the first $i$ vertices of $\\pi$. The cutwidth of $\\pi$ is $ctw(D\,\\pi) = \\max_{i \\in [n]} D(\\pi\,i)$ and the cutwidth of $D$ is $ctw(D) = \\mi n_{\\pi} ctw(D\,\\pi)$.\n\nAs for many width measures\, computing the cutw idth is NP-Hard in general. We will prove it remains true even in the semi -complete case\, but that computing the cutwidth of a tournament is polyno mial. From these results\, we will show how to approximate the cutwidth of a semi-complete digraph (in a non-linear manner\, however)\, or how to co nstruct small tournaments with a fixed cutwidth. We will also show that an y tournament contains a sub-tournament with same cutwidth $c$ and size at most linear in $c$. Finally\, we will study some generalization of {\\sc F eedback Vertex/Edge Deletion}\, called {\\sc Cutwidth Vertex Deletion} and {\\sc Cutwidth Arc Reversal} (restricted to semi-complete digraph). LAST-MODIFIED;VALUE=DATE-TIME:20160210T090103Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/f90d6688-4d93-45b0-982d-cf46ec5411fc END:VEVENT BEGIN:VEVENT SUMMARY:Lucia Penso\, «Geodetic convexity parameters for graphs with few short induced paths» DTSTART;VALUE=DATE-TIME:20160929T080000Z DTEND;VALUE=DATE-TIME:20160929T100000Z DTSTAMP;VALUE=DATE-TIME:20160915T092742Z UID:8f97ad47-f618-47c3-bb65-e54ce124f019 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20160915T092742Z DESCRIPTION:We study parameters of geodetic convexity for graph classes de fined by restrictions concerning short induced paths. We show that computi ng the geodetic hull number of a given $P_9$-free graph is NP-hard. Simila rly\, we show that computing the geodetic interval number of a given $P_5$ -free graph is NP-hard. On the positive side\, we identify several graph c lasses for which the geodetic hull number can be computed efficiently. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/8f97ad47-f618-47c3-bb65-e54ce124f019 END:VEVENT BEGIN:VEVENT SUMMARY:La Xuan Hoang\, «TBA» DTSTART;VALUE=DATE-TIME:20090616T220000Z DTEND;VALUE=DATE-TIME:20090617T220000Z DTSTAMP;VALUE=DATE-TIME:20190516T093433Z UID:ce475406-a026-4597-bc24-215b08ee24a6 SEQUENCE:2 CREATED;VALUE=DATE-TIME:20190516T093433Z DESCRIPTION:TBA LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/ce475406-a026-4597-bc24-215b08ee24a6 END:VEVENT BEGIN:VEVENT SUMMARY:DeMoGraph\, «Réunion de lancement de l'ANR DeMoGraph» DTSTART;VALUE=DATE-TIME:20170517T080000Z DTEND;VALUE=DATE-TIME:20170518T160000Z DTSTAMP;VALUE=DATE-TIME:20170405T100734Z UID:d3ebcaad-1ab3-4577-8710-cebd8074dc20 SEQUENCE:2 CREATED;VALUE=DATE-TIME:20170405T100734Z DESCRIPTION:Réunion de lancement de l'ANR DeMoGraph LAST-MODIFIED;VALUE=DATE-TIME:20170516T080104Z LOCATION: URL:https://info-web.lirmm.fr/collorg/d3ebcaad-1ab3-4577-8710-cebd8074dc20 END:VEVENT BEGIN:VEVENT SUMMARY:Matthieu Rosenfeld\, «Every long enough binary pattern is abelian 2-avoidable» DTSTART;VALUE=DATE-TIME:20160225T090000Z DTEND;VALUE=DATE-TIME:20160225T103000Z DTSTAMP;VALUE=DATE-TIME:20160219T170228Z UID:8fbd04be-6b47-4b7d-82e9-ba3bf1a9ef2b SEQUENCE:4 CREATED;VALUE=DATE-TIME:20160219T170228Z DESCRIPTION:We say that two words u and v are abelian equivalent if they h ave the same number of occurrences of each letter (i.e.\, they are permuta tions or anagrams). I will define what it means to avoid a pattern in the abelian sense. The interest in this topic is due to Erdös asking whether the pattern AA can be avoided in the abelian sense by an infinite words ov er 4 letters (the answer is yes). We obtain that every binary pattern of s ize at least 16 can be avoided by an infinite binary word. LAST-MODIFIED;VALUE=DATE-TIME:20160224T090103Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/8fbd04be-6b47-4b7d-82e9-ba3bf1a9ef2b END:VEVENT BEGIN:VEVENT SUMMARY:Pas de séminaire (JCALMs)\, «TBA» DTSTART;VALUE=DATE-TIME:20160310T090000Z DTEND;VALUE=DATE-TIME:20160310T091500Z DTSTAMP;VALUE=DATE-TIME:20160223T165508Z UID:98c43447-2ecb-43f6-bd2f-2e1461067fb6 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20160223T165508Z DESCRIPTION:TBA LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION: URL:https://info-web.lirmm.fr/collorg/98c43447-2ecb-43f6-bd2f-2e1461067fb6 END:VEVENT BEGIN:VEVENT SUMMARY:Marcin Pilipczuk \, «Recent progress in distance and cut sparsifi ers.» DTSTART;VALUE=DATE-TIME:20170921T080000Z DTEND;VALUE=DATE-TIME:20170921T090000Z DTSTAMP;VALUE=DATE-TIME:20170529T143511Z UID:5370a4ea-0a2d-4379-b4d7-a99f0b55b87f SEQUENCE:2 CREATED;VALUE=DATE-TIME:20170529T143511Z DESCRIPTION:In the talk I will discuss two related notions with regards to graph compression.\n- Given a graph (directed or undirected\, weighted or unweighted) G with n vertices\, and a set P of p pairs of vertices\, a di stance sparsifier is an edge-minimal subgraph of G that maintains the same lengths of shortest paths between the pairs in P. A natural question is t o obtain as small as possible size of a distance sparsifier\, expressed as a function of n and p. \n- Given an edge-weighted graph G with a set Q of k terminals\, a mimicking network is a graph with the same set of termina ls that exactly preserves the sizes of minimum cuts between any partition of the terminals. A natural question in the area of graph compression is t o provide as small mimicking networks as possible for input graph G being either an arbitrary graph or coming from a specific graph class. \nIn many special cases\, the known upper and lower bounds for the above concepts a re surprising far from each other. In the talk\, I will survey these areas \, with emphasize on open problems. Furthermore\, I will present our recen t result obtained in a joint work with Nikolai Karpov and Anna Zych-Pawlew icz\, namely an exponential lower bound for cut mimicking networks in plan ar graphs: there are edge-weighted planar graphs with k terminals that req uire 2^{k−2} edges in any mimicking network. LAST-MODIFIED;VALUE=DATE-TIME:20170920T080104Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/5370a4ea-0a2d-4379-b4d7-a99f0b55b87f END:VEVENT BEGIN:VEVENT SUMMARY:Eunjung Kim\, «The “art of trellis decoding” is fixed-paramet er tractable» DTSTART;VALUE=DATE-TIME:20160324T090000Z DTEND;VALUE=DATE-TIME:20160324T103000Z DTSTAMP;VALUE=DATE-TIME:20160304T160359Z UID:db94592c-6ec5-4eb5-a3ae-2ab07d7b89d9 SEQUENCE:0 CREATED;VALUE=DATE-TIME:20160304T160359Z DESCRIPTION:Given n subspaces of a finite-dimensional vector space over a fixed finite field 𝔽\, we wish to find a linear layout V1\,V2\,…\,Vn of the subspaces such that dim((V1+V2+⋯+Vi)∩(Vi+1+⋯+Vn))≤k for all i\, such a linear layout is said to have width at most k. When restricted to 1-dimensional subspaces\, this problem is equivalent to computing the trellis-width (or minimum trellis state-complexity) of a linear code in co ding theory and computing the path-width of an 𝔽-represented matroid in matroid theory. \n\nWe present a fixed-parameter tractable algorithm to c onstruct a linear layout of width at most k\, if it exists\, for input sub spaces of a finite-dimensional vector space over 𝔽. As corollaries\, we obtain a fixed-parameter tractable algorithm to produce a path-decomposit ion of width at most k for an input 𝔽-represented matroid of path-width at most k\, and a fixed-parameter tractable algorithm to find a linear ra nk-decomposition of width at most k for an input graph of linear rank-widt h at most k. In both corollaries\, no such algorithms were known previousl y. \n\nIt was previously known that a fixed-parameter tractable algorithm exists for the decision version of the problem for matroid path-width\, a theorem by Geelen\, Gerards\, and Whittle (2002) implies that for each fix ed finite field 𝔽\, there are finitely many forbidden 𝔽-representabl e minors for the class of matroids of path-width at most k. An algorithm b y Hliněný (2006) can detect a minor in an input 𝔽-represented matroid of bounded branch-width. However\, this indirect approach would not produ ce an actual path-decomposition. Our algorithm is the first one to constru ct such a path-decomposition and does not depend on the finiteness of forb idden minors. LAST-MODIFIED;VALUE=DATE-TIME:20160323T090103Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/db94592c-6ec5-4eb5-a3ae-2ab07d7b89d9 END:VEVENT BEGIN:VEVENT SUMMARY:Stéphan Thomassé\, «Computing Maximum Independent Set in Graph Classes» DTSTART;VALUE=DATE-TIME:20190523T080000Z DTEND;VALUE=DATE-TIME:20190523T090000Z DTSTAMP;VALUE=DATE-TIME:20190410T095613Z UID:df6b58a9-da9c-469e-aa72-008713ae9b9e SEQUENCE:1 CREATED;VALUE=DATE-TIME:20190410T095613Z DESCRIPTION:Computing MIS in graph classes is often the right approach for many optimization problems. For instance finding a near maximal set of pa irwise intersecting disks in the plane can be done in polytime\, just by c onsidering the intersection graph structure. While this approach is appeal ing\, the general problem "Decide which classes C of graphs are easy for M IS" seems a very difficult task. A first and more modest step is to restri ct ourselves to classes C defined by a finite list of forbidden induced su bgraphs. Here we could show with M. Chudnowsky\, M. Pilipczuk and M. Pilip czuk that MIS in Pt-free graphs admits a QPTAS\, and this led to a general dichotomy: MIS is either APX-hard or has a QPTAS. Strenghtening QPTAS for these classes to PTAS\, QP or even P seems however hard\, as a very fine understanding is needed. A much more difficult problem is to characterize these classes C for which MIS is FPT. Sadly\, even if we can now decide if MIS is FPT in H-free graphs\, where H has at most 5 vertices\, we have ne ither a candidate for a general characterization\, nor a general type of a lgorithm. Instead we face many different aspects of computing an independe nt set\, which makes this question a very exciting playground (Joint work with E. Bonnet\, N. Bousquet\, P. Charbit and R. Watrigant). LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/df6b58a9-da9c-469e-aa72-008713ae9b9e END:VEVENT BEGIN:VEVENT SUMMARY:Guillaume Guégan\, «From tournaments to unifom oriented matroids and vice versa» DTSTART;VALUE=DATE-TIME:20160317T093000Z DTEND;VALUE=DATE-TIME:20160317T103000Z DTSTAMP;VALUE=DATE-TIME:20160211T101939Z UID:be98570b-9480-43c4-8676-e92599394fa8 SEQUENCE:3 CREATED;VALUE=DATE-TIME:20160211T101939Z DESCRIPTION:Locally transitive tournaments (LTT) are reorientations of the transitive tournament. Despite being a simple class to describe\, they ha ve rich and deep combinatorics. Uniform oriented matroids (UOM) can be und erstood as collections of LTT. I will present a new characterization of LT T which has a deep impact on the theory of UOMs:\n1) the creation of new a nd interesting invariants\; \n2) characterization of lambda-functions of U OM (generalizing scores of tournaments). LAST-MODIFIED;VALUE=DATE-TIME:20160316T093102Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/be98570b-9480-43c4-8676-e92599394fa8 END:VEVENT BEGIN:VEVENT SUMMARY:Julien Baste\, «The number of labeled graphs of bounded treewidth » DTSTART;VALUE=DATE-TIME:20160331T080000Z DTEND;VALUE=DATE-TIME:20160331T093000Z DTSTAMP;VALUE=DATE-TIME:20160107T112808Z UID:e83bc7b7-8d2f-447c-9b9e-72cff0d6386d SEQUENCE:19 CREATED;VALUE=DATE-TIME:20160107T112808Z DESCRIPTION:Treewidth is undoubtedly one of the most fundamental parameter s in modern graph theory and algorithms. Its theoretical importance is dem onstrated by its crucial role in the proof of the Graph Minor theorem by R oberston and Seymour\, while its algorithmic relevance is certified\, for instance\, by Courcelle's theorem. \n\nIn this talk we focus on couting th e number of labeled graphs on $n$ vertices and treewidth $k$\, which we de note by $T_{n\,k}$. So far\, only the particular cases $T_{n\,1}$ and $T_{ n\,2}$ had been studied. Using a construction that exploits the fact that a graph has treewidth at most $k$ if and only if it is a partial $k$-tree\ , we show that\n\n$$\\left(c \\cdot \\frac{k}{\\log k} \\cdot 2^k \\cdot n \\right)^n \\cdot 2^{-k(k+1)/2} \\cdot k^{-2k-2}\\ \\leq\\ T_{n\,k}\\ \\l eq\\ \\left(k \\cdot 2^k \\cdot n\\right)^n \\cdot 2^{-k(k+1)/2} \\cdot k^ {-k}\,$$\n\nfor some explicit constant $c > 0$. Our results also apply to graphs of pathwidth at most $k$. \n\nJoint work with Marc Noy and Ignasi S au. LAST-MODIFIED;VALUE=DATE-TIME:20160330T080103Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/e83bc7b7-8d2f-447c-9b9e-72cff0d6386d END:VEVENT BEGIN:VEVENT SUMMARY:Bastien Cazaux\, «The Superstring Graph» DTSTART;VALUE=DATE-TIME:20160428T080000Z DTEND;VALUE=DATE-TIME:20160428T093000Z DTSTAMP;VALUE=DATE-TIME:20160322T161952Z UID:ef6bedca-ee62-446e-9292-7a8d1ca3c259 SEQUENCE:0 CREATED;VALUE=DATE-TIME:20160322T161952Z DESCRIPTION:Merging words according to their overlap yields a superstring. This basic operation allows to infer long strings from a collection of sh ort pieces\, as in genome assembly. To capture a maximum of overlaps\, the goal is to infer the shortest superstring of a set of input words. The Sh ortest Cyclic Cover of Strings (SCCS) problem asks\, instead of a single l inear superstring\, for a set of cyclic strings that contain the words as substrings and whose sum of lengths is minimal. SCCS is used as a crucial step in polynomial time approximation algorithms for the notably hard Shor test Superstring problem\, but it is solved in cubic time. The cyclic stri ngs are then cut and merged to build a linear superstring. Building on rec ent theoretical work\, I will present you a linear time algorithm for solv ing SCCS based on a Eulerian graph (the Superstring Graph) that captures a ll greedy solutions in linear space. LAST-MODIFIED;VALUE=DATE-TIME:20160427T080103Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/ef6bedca-ee62-446e-9292-7a8d1ca3c259 END:VEVENT BEGIN:VEVENT SUMMARY:Giannos Stamoulis\, «Block Elimination Distance» DTSTART;VALUE=DATE-TIME:20210701T080000Z DTEND;VALUE=DATE-TIME:20210701T090000Z DTSTAMP;VALUE=DATE-TIME:20210607T154607Z UID:9e20026e-cf26-4db4-a0e6-40a0c63a0a43 SEQUENCE:6 CREATED;VALUE=DATE-TIME:20210607T154607Z DESCRIPTION:We introduce the parameter of //block elimination distance// a s a measure of how close a graph is to some particular graph class. Forma lly\, given a graph class ${\\cal G}$\, the class ${\\cal B}({\\cal G})$ c ontains all graphs whose blocks belong to ${\\cal G}$ and the class ${\\ca l A}({\\cal G})$ contains all graphs where the removal of a vertex creates a graph in ${\\cal G}$. Given a hereditary graph class ${\\cal G}$\, we r ecursively define ${\\cal G}^{(k)}$ so that ${\\cal G}^{(0)}={\\cal B}({\\ cal G})$ and\, if $k\\geq 1$\, ${\\cal G}^{(k)}={\\cal B}({\\cal A}({\\cal G}^{(k-1)}))$. The //block elimination distance//\, denoted by ${\\bf bed }(G)$ of a graph $G$ to a graph class ${\\cal G}$ is the minimum $k$ such that $G\\in{\\cal G}^{(k)}$ and can be seen as an analog of the eliminat ion distance parameter\, defined in //[J. Bulian and A. Dawar. Algorithmi ca\, 75(2):363–382\, 2016]//\, with the difference that connectivity is now replaced by biconnectivity. We show that\, for every non-trivial her editary class ${\\cal G}$\, the problem of deciding whether $G\\in{\\cal G}^{(k)}$ is {\\sf NP}-complete. We focus on the case where ${\\cal G}$ is minor-closed and we study the minor obstruction set of ${\\cal G}^{(k)} $ i.e.\, the minor-minimal graphs not in ${\\cal G}^{(k)}$. We prove that the size of the obstructions of ${\\cal G}^{(k)}$ is upper bounded by some explicit function of $k$ and the maximum size of a minor obstruction of ${\\cal G}$. This implies that the problem of deciding whether $G\\in{\\c al G}^{(k)}$ is //constructively// fixed parameter tractable\, when parame terized by $k$. Our results are based on a structural characterization of the obstructions of ${\\cal B}({\\cal G})$\, relatively to the obstruction s of ${\\cal G}$. Finally\, we give two graph operations that generate me mbers of ${\\cal G}^{(k)}$ from members of ${\\cal G}^{(k-1)}$ and we pro ve that this set of operations is complete for the class ${\\cal O}$ of ou terplanar graphs. This yields the //identification// of all members ${\\ca l O}\\cap{\\cal G}^{(k)}$\, for every $k\\in\\mathbb{N}$ and every non-tri vial minor-closed graph class ${\\cal G}$.\n\n\nJoint work with Öznur Ya şar Diner\, Archontia C. Giannopoulou\, and Dimitrios M. Thilikos\nDimitr ios M. Thilikos LAST-MODIFIED;VALUE=DATE-TIME:20210630T080102Z LOCATION:https://bbb.lirmm.fr/b/dim-ajj-ddd URL:https://info-web.lirmm.fr/collorg/9e20026e-cf26-4db4-a0e6-40a0c63a0a43 END:VEVENT BEGIN:VEVENT SUMMARY:Ignasi Sau\, «Finding subdivisions of spindles on digraphs.» DTSTART;VALUE=DATE-TIME:20171026T080000Z DTEND;VALUE=DATE-TIME:20171026T090000Z DTSTAMP;VALUE=DATE-TIME:20171018T063406Z UID:befa9189-8d46-4117-8ff3-43250acb1b93 SEQUENCE:4 CREATED;VALUE=DATE-TIME:20171018T063406Z DESCRIPTION:For two positive integers $k$ and $\\ell$\, a $(k \\times \\el l)$-spindle is the union of $k$ pairwise internally vertex-disjoint direct ed paths with $\\ell$ arcs between two vertices $u$ and $v$. In this talk we are interested in the (parameterized) complexity of several problems co nsisting in deciding whether a given digraph contains a subdivision of a s pindle\, which generalize both the Maximum Flow and Longest Path problems. \n\nWe obtain the following complexity dichotomy: for a fixed $\\ell \\geq 1$\, finding the largest $k$ such that an input digraph $G$ contains a su bdivision of a $(k \\times \\ell)$-spindle is polynomial-time solvable if $\\ell \\leq 3$\, and NP-hard otherwise. We place special emphasis on find ing spindles with exactly two paths and present FPT algorithms that are as ymptotically optimal under the ETH. These algorithms are based on the tech nique of representative families in matroids\, and use also color-coding a s a subroutine. Finally\, we study the case where the input graph is acycl ic\, and prove several positive and negative results.\n\nJoint work with J úlio Araújo\, Victor A. Campos\, Ana Karolinna Maia\,\nand Ana Silva. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION: URL:https://info-web.lirmm.fr/collorg/befa9189-8d46-4117-8ff3-43250acb1b93 END:VEVENT BEGIN:VEVENT SUMMARY:Petr A. Golovach\, «Parameterized Low-Rank Binary Matrix Approxi mation» DTSTART;VALUE=DATE-TIME:20190926T080000Z DTEND;VALUE=DATE-TIME:20190926T090000Z DTSTAMP;VALUE=DATE-TIME:20190925T065452Z UID:b7ecc070-d325-4dcf-aa88-9757cf888cd4 SEQUENCE:0 CREATED;VALUE=DATE-TIME:20190925T065452Z DESCRIPTION:(joint work with Fedor V. Fomin and Fahad Panolan) \n\nWe pro vide a number of algorithmic results for the following family of problems : For a given binary m\\times n matrix A and integer k\, decide whether th ere is a ``simple'' binary matrix B which differs from A in at most k en tries. For an integer r\, the ``simplicity'' of B is characterized as f ollows.\n\n- Binary r-Means: Matrix B has at most r different columns. This problem is known to be NP-complete already for r=2. We show that the problem is solvable in time 2^{O(k\\log k)}(nm)^{O(1)} and thus is fixed-p arameter tractable parameterized by k. We prove that the problem admits a polynomial kernel when parameterized by r and k but it has no polynomial kernel when parameterized by k only unless NP\\subseteq CoNP/ poly}. We al so complement these result by showing that when being parameterized by r a nd k\, the problem admits an algorithm of running time 2^{O( \\sqrt{kr\\l og{(k+r)\\log r}})}(nm)^{O(1)}\, which is subexponential in k. \n\n- Lo w GF(2)-Rank Approximationt: Matrix B is of GF(2)-rank at most r. This problem is known to be NP-complete already for r=1. It is also known to be W[1]-hard when parameterized by k. Interestingly\, when parameterized by r and k\, the problem is not only fixed-parameter tractable\, but it is so lvable in time 2^{O(r\\sqrt{k\\log{kr}})}(nm)^{O(1)}\, which is subexpo nential in k. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/b7ecc070-d325-4dcf-aa88-9757cf888cd4 END:VEVENT BEGIN:VEVENT SUMMARY:Marin Bougeret\, «How much does a treedepth modulator help to obt ain polynomial kernels?» DTSTART;VALUE=DATE-TIME:20180308T090000Z DTEND;VALUE=DATE-TIME:20180308T100000Z DTSTAMP;VALUE=DATE-TIME:20180202T091111Z UID:5a813021-55cc-4f6b-a099-f6e35d9095cb SEQUENCE:6 CREATED;VALUE=DATE-TIME:20180202T091111Z DESCRIPTION:In the last years\, kernelization with structural parameters h as been an active area of research within the field of parameterized compl exity. As a relevant example\, Gajarsky et al [ESA 2013] proved that every graph problem satisfying a property called finite integer index admits a linear kernel on graphs of bounded expansion and an almost linear kernel o n nowhere dense graphs\, parameterized by the size of a $c$-treedepth modu lator\, which is a vertex set whose removal results in a graph of treedept h at most $c$\, where $c \\geq 1$ is a fixed integer. The authors left as further research to investigate this parameter on general graphs\, and in particular to find problems that\, while admitting polynomial kernels on s parse graphs\, behave differently on general graphs.\n\nIn this article we answer this question by finding two very natural such problems: we prove that Vertex Cover admits a polynomial kernel on general graphs for any int eger $c \\geq 1$\, and that Dominating Set does not for any integer $c \\g eq 2$ even on degenerate graphs\, unless $\\text{NP} \\subseteq \\text{coN P}/\\text{poly}$. For the positive result\, we build on the techniques of Jansen and Bodlaender [STACS 2011]\, and for the negative result we use a polynomial parameter transformation for $c\\geq 3$ and an or-cross-composi tion for $c = 2$. As existing results imply that Dominating Set admits a p olynomial kernel on degenerate graphs for $c = 1$\, our result provides a dichotomy about the existence of polynomial kernels for Dominating Set on degenerate graphs with this parameter.\n\nThis is a joint work with Ignasi Sau. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/5a813021-55cc-4f6b-a099-f6e35d9095cb END:VEVENT BEGIN:VEVENT SUMMARY:Dimitrios M. Thilikos\, «A Detaild Exposition of The Flat Wall th eorem» DTSTART;VALUE=DATE-TIME:20200604T090000Z DTEND;VALUE=DATE-TIME:20200604T100000Z DTSTAMP;VALUE=DATE-TIME:20200309T194639Z UID:94d68bc8-8498-4462-b794-1e23d09193ac SEQUENCE:30 CREATED;VALUE=DATE-TIME:20200309T194639Z DESCRIPTION:The Flat Wall theorem was proved by Roberston and Seymour as p art of their Graph Minors series (GM XIII). This theorem reveals that ever y graph excluding a clique as a minor and having sufficiently big treewidt h contains a "flat wall"\, that is subdivision of a wall that is arranged inside the graph in a "flat manner''. In the same paper\, this theorem was used as a key graph-structural ingredient of an algorithm for the celebra ted Disjoint Paths Problem. GM XIII was published in J. Comb. Theory Ser. B in 1995 and since then\, this theorem was used in numerous applications both in combinatorics and in algorithmic design. The purpose of this semin ar is to give a detailed and precise statement of the Flat Wall Theorem\, accompanied with a comparative study of its various alternative forms\, op timizations\, and applications. \n\n\nhttps://moodle.umontpellier.fr/enrol /index.php?id=15640 LAST-MODIFIED;VALUE=DATE-TIME:20210125T145759Z LOCATION:Téléseminaire URL:https://info-web.lirmm.fr/collorg/94d68bc8-8498-4462-b794-1e23d09193ac END:VEVENT BEGIN:VEVENT SUMMARY:Amadeus Reinald\, «Twin-width: forbidden subdivisions and polynom ial kernels» DTSTART;VALUE=DATE-TIME:20211202T090000Z DTEND;VALUE=DATE-TIME:20211202T100000Z DTSTAMP;VALUE=DATE-TIME:20211019T115400Z UID:5621430f-e675-40e4-b624-a69a5a33447d SEQUENCE:4 CREATED;VALUE=DATE-TIME:20211019T115400Z DESCRIPTION:Twin-width is a recently introduced graph parameter based on v ertex contraction sequences. On classes of bounded twin-width\, FO model c hecking is FPT when provided with a sequence witnessing the bound. In this talk\, we first explore the structure implied by large twin-width in term s of induced subdivisions\, to then look at the existence of polynomial ke rnels on classes of bounded twin-width.\n\nStructurally\, the understandin g of graph parameters in terms of induced subgraphs\, rather than minors\, is an active area of research. For treewidth\, an induced analogue of the grid minor theorem could be that\, for sparse graphs\, large treewidth im plies the existence of an induced subdivision of a large wall. However\, S intiari and Trotignon have ruled out such a characterization by showing th e existence of graphs with arbitrarily large girth avoiding any induced su bdivision of a theta ($K_{2\,3}$). Abrishami\, Chudnovsky\, Hajebi and Spi rkl have recently shown that such (theta\, triangle)-free classes have nev ertheless logarithmic treewidth. Through a structural "Connected-BFS" deco mposition\, we show that theta-free graphs of girth at least 5 have bounde d twin-width.\n\nWe then study the existence of polynomial kernels for k-D ominating Set and variants of k-Vertex Cover on classes of bounded twin-wi dth. Our main result is that k-Dominating Set admits no polynomial kernel on graphs of twin-width at most 4. On the positive side\, we leverage a VC -density argument on classes of bounded twin-width to show that Connected k-Vertex Cover and Capacitated k-Vertex Cover admit $O(k^1.5)$ and $O(k^2) $ kernels respectively.\n\nJoint work with Édouard Bonnet\, Eun Jung Kim\ , Stéphan Thomassé and Rémi Watrigant. LAST-MODIFIED;VALUE=DATE-TIME:20211201T090103Z LOCATION:BAT4 l Séminaire LIRMM - RDC Entrée & https://bbb.lirmm.fr/b/di m-ajj-ddd URL:https://info-web.lirmm.fr/collorg/5621430f-e675-40e4-b624-a69a5a33447d END:VEVENT BEGIN:VEVENT SUMMARY:Didem Gözüpek\, «Recent Results on Equimatchable Graphs» DTSTART;VALUE=DATE-TIME:20160526T080000Z DTEND;VALUE=DATE-TIME:20160526T093000Z DTSTAMP;VALUE=DATE-TIME:20160503T135410Z UID:b93b3394-f012-4378-88fc-0af83bef412d SEQUENCE:2 CREATED;VALUE=DATE-TIME:20160503T135410Z DESCRIPTION:A graph is equimatchable if all of its maximal matchings have the same size. In this talk\, I will present some recent results on equima tchable graphs such as forbidden subgraphs\, stable equimatchable graphs\, and the characterization of claw-free equimatchable graphs. I will then d iscuss about some new research directions. LAST-MODIFIED;VALUE=DATE-TIME:20160525T080102Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/b93b3394-f012-4378-88fc-0af83bef412d END:VEVENT BEGIN:VEVENT SUMMARY:Pas de séminaire (école CIRM)\, «TBA» DTSTART;VALUE=DATE-TIME:20160512T080000Z DTEND;VALUE=DATE-TIME:20160512T090000Z DTSTAMP;VALUE=DATE-TIME:20160503T135010Z UID:967676a7-a9d7-46aa-8599-2a53b70be298 SEQUENCE:0 CREATED;VALUE=DATE-TIME:20160503T135010Z DESCRIPTION:TBA LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION: URL:https://info-web.lirmm.fr/collorg/967676a7-a9d7-46aa-8599-2a53b70be298 END:VEVENT BEGIN:VEVENT SUMMARY:Ilda Perez Fernandez da Silva\, «Shannon switching game and direc ted variants» DTSTART;VALUE=DATE-TIME:20160602T080000Z DTEND;VALUE=DATE-TIME:20160602T093000Z DTSTAMP;VALUE=DATE-TIME:20160418T154411Z UID:2a5720f0-c067-4fef-8d6e-9b469036f04b SEQUENCE:4 CREATED;VALUE=DATE-TIME:20160418T154411Z DESCRIPTION:The “classical” Shannon switching game is a combinatorial game invented by C. Shannon in the 1950’s. The game was completely solv ed by A. Lehman\, shortly after\, in what is considered the first applicat ion of matroid theory. In the middle 1980’s Y. O. Hamidoune and M. Las V ergnas studied and solved directed versions of the game for graphs conside ring their generalization to oriented matroids. Recently with some colleag ues and students of Informatics we made some proptotypes of computational implementations of the games. We will do a brief review of the main result s and conjectures concerning the directed case.\n\nReference:\nA. P. Cláu dio\, S. Fonseca\, L. Sequeira\, I.P. Silva\, Shannon switching\nGame and directed variants\, in Bourguignon\, J.-P.\, Jeltsch\, R.\, Pinto\,\nA.A.\ , Viana\, M. (Eds.) Dynamics\, Games and Science II\, CIM Series\nin Mathe matical Science 1\, Springer 2015\, 187-199. LAST-MODIFIED;VALUE=DATE-TIME:20160601T080104Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/2a5720f0-c067-4fef-8d6e-9b469036f04b END:VEVENT BEGIN:VEVENT SUMMARY:Uéverton S. Souza \, «Computing the largest bond of a graph» DTSTART;VALUE=DATE-TIME:20191106T090000Z DTEND;VALUE=DATE-TIME:20191106T100000Z DTSTAMP;VALUE=DATE-TIME:20191009T114053Z UID:ee13a654-26b1-4977-a5ca-8c7fe93cc7d1 SEQUENCE:2 CREATED;VALUE=DATE-TIME:20191009T114053Z DESCRIPTION:A bond of a graph G is an inclusion-wise minimal disconnecting set of G\, i.e.\, bonds are cut-sets that determine cuts [S\, V \\ S] of G such that G[S] and G[V \\ S] are both connected. Given s\,t \\in V(G)\, an st-bond of G is a bond whose removal disconnects s and t. Contrasting w ith the large number of studies related to maximum cuts\, there are very f ew results regarding the largest bond of general graphs. In this paper\, w e aim to reduce this gap on the complexity of computing the largest bond a nd the largest st-bond of a graph. Although cuts and bonds are similar\, w e remark that computing the largest bond of a graph tends to be harder tha n computing its maximum cut. We show that Largest Bond remains NP-hard eve n for planar bipartite graphs\, and it does not admit a constant-factor ap proximation algorithm\, unless P = NP. We also show that Largest Bond and Largest st-Bond on graphs of clique-width w cannot be solved in time f(w) × n^{o(w)} unless the Exponential Time Hypothesis fails\, but they can be solved in time f(w) × n^{O(w)}. In addition\, we show that both problems are fixed-parameter tractable when parameterized by the size of the solut ion\, but they do not admit polynomial kernels unless NP \\subseteq coNP/ poly. \n\nJoint work with Gabriel L. Duarte\, Daniel Lokshtanov\, Lehilton L. C. Pedrosa\, and Rafael C. S. Schouery. LAST-MODIFIED;VALUE=DATE-TIME:20191105T090104Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/ee13a654-26b1-4977-a5ca-8c7fe93cc7d1 END:VEVENT BEGIN:VEVENT SUMMARY:Lucas Isenmann\, «Dushnik-Miller dimension of TD-Delaunay complex es» DTSTART;VALUE=DATE-TIME:20170330T080000Z DTEND;VALUE=DATE-TIME:20170330T090000Z DTSTAMP;VALUE=DATE-TIME:20170303T142142Z UID:f074cc4a-5f86-4fa8-9b3b-d342ea20a5c7 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20170303T142142Z DESCRIPTION:TD-Delaunay graphs\, where TD stands for triangle-distance\, a re obtained from a variation of Delaunay triangulation consisting in repla cing circles by homothetic triangles. It was noticed that every triangulat ion is the TD-Delaunay graph of a set of points in R^2\, and conversely. I t seems natural to study the generalization of this property in higher dim ensions. Such a generalization is obtained by replacing equilateral triang les by regular simplexes in dimension R^d. The abstract simplicial complex es obtained from a TD-Delaunay complex in dimension d are of Dushnik-Mille r dimension d + 1. The converse holds for d = 2 and 3 and it was conjectur ed to hold for larger d. Our work with Daniel Gonçalves is to disprove th e conjecture already for d = 4. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/f074cc4a-5f86-4fa8-9b3b-d342ea20a5c7 END:VEVENT BEGIN:VEVENT SUMMARY:Ana Silva\, «Graphs with small fall-spectrum» DTSTART;VALUE=DATE-TIME:20190117T090000Z DTEND;VALUE=DATE-TIME:20190117T100000Z DTSTAMP;VALUE=DATE-TIME:20181220T153131Z UID:6b77af7d-d372-4577-8a64-1f53e956c08c SEQUENCE:3 CREATED;VALUE=DATE-TIME:20181220T153131Z DESCRIPTION:Given a proper coloring $f$ of a graph $G$\, a b-vertex in $f$ is a vertex that is adjacent to every color class but its own\, and $f$ i s a fall-coloring if every vertex is a b-vertex. The fall-spectrum of $G$ is the set $\\F(G)$ of all values $k$ for which $G$ admits a fall-coloring with $k$ colors. Some authors have found that some subclasses of perfect graphs have the property that: \n\n(*) $\\F(G)\\neq\\emptyset$ if and only if $\\chi(G)=\\delta(G)+1$. \n\nThis has led Kaul and Mitilos to conjectu re that (*) holds for every perfect graph. We prove that this is not true by showing a chordal graph on which (*) does not hold. Nevertheless\, we i nvestigate what is the "good property" that these graphs have and\, among other results\, we have found some interesting aspects that led us to intr oduce perfectness classes related to this kind of coloring. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/6b77af7d-d372-4577-8a64-1f53e956c08c END:VEVENT BEGIN:VEVENT SUMMARY:Guilherme Gomes\, «Parameterized Complexity of Equitable Coloring and Intersection Graphs of maximal stars» DTSTART;VALUE=DATE-TIME:20180913T080000Z DTEND;VALUE=DATE-TIME:20180913T090000Z DTSTAMP;VALUE=DATE-TIME:20180831T073003Z UID:f0706c1e-233e-46b9-a792-53c46a912045 SEQUENCE:6 CREATED;VALUE=DATE-TIME:20180831T073003Z DESCRIPTION:A n-vertex graph is equitably k-colorable if it admits a prope r k-coloring such the size of any two color classes differ by at most one. We present some results on parameterized complexity of the problem for su bclasses of chordal graphs\, showing that even if we parameterize by the n umber of colors\, treewidth and maximum degree\, equitably coloring a K_1\ ,4-free interval graph is W[1]-Hard. This generalizes a result by Fellows et al. (2014) through a much simpler reduction. Together with a theorem du e to de Werra (1985)\, we establish a dichotomy for the parameterized comp lexity of equitably coloring chordal graphs based on the size of the large st induced star. Finally\, we give an FPT algorithm for equitable coloring parameterized by the treewidth of the complement graph\, which has optima l running time (up to polynomial factors) unless ETH fails.\n\nOutside par ameterized complexity\, we investigate a problem in intersection graph the ory\, namely the characterization and recognition of the intersection grap hs of maximal stars. We provide a Krausz-type characterization for the cla ss by showing that a small set of natural conditions is both necessary and sufficient. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/f0706c1e-233e-46b9-a792-53c46a912045 END:VEVENT BEGIN:VEVENT SUMMARY:Dimitrios Thilikos\, «Cutwidth: obstructions and algorithmic aspe cts» DTSTART;VALUE=DATE-TIME:20161208T090000Z DTEND;VALUE=DATE-TIME:20161208T100000Z DTSTAMP;VALUE=DATE-TIME:20160930T073005Z UID:fe52d6ea-4007-42c8-b7ab-b4859e91cbc1 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20160930T073005Z DESCRIPTION:Cutwidth is one of the classic layout parameters for graphs. I t measures how well one can order the vertices of a graph in a linear mann er\, so that the maximum number of edges between any prefix and its comple ment suffix is minimized. As graphs of cutwidth at most k are closed under taking immersions\, the results of Robertson and Seymour imply that there is a finite list of minimal immersion obstructions for admitting a cut la yout of width at most k. \n\nWe prove that every minimal immersion obstruc tion for cutwidth at most k has size at most $2^{O(k^3 log k)}$. For our p roof\, we introduce the concept of a lean ordering that can be seen as the analogue of lean decompositions defined by Thomas in [A Menger-like prope rty of tree-width: The finite case\, J. Comb. Theory\, Ser. B\, 48(1):67 –76\, 1990] for the case of treewidth. As an interesting algorithmic byp roduct\, we design a new fixed-parameter algorithm for computing the cutwi dth of a graph that runs in time $2^{O(k^2 log k)} · n$\, where k is the optimum width and n is the number of vertices. While being slower by a log k-factor in the exponent than the fastest known algorithm\, given by Thil ikos\, Bodlaender\, and Serna in [Cutwidth I: A linear time fixed paramete r algorithm\, J. Algorithms\, 56(1):1–24\, 2005] and [Cutwidth II: Algor ithms for partial w-trees of bounded degree\, J. Algorithms\, 56(1):25–4 9\, 2005]\, our algorithm has the advantage of being simpler and self-cont ained\; arguably\, it explains better the combinatorics of optimum-width l ayouts.\n\nJoined work with Archontia C. Giannopoulou\, Michał Pilipczuk\ , Jean-Florent Raymond\, and Marcin Wrochna LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/fe52d6ea-4007-42c8-b7ab-b4859e91cbc1 END:VEVENT BEGIN:VEVENT SUMMARY:Dieter Rautenbach\, «On the maximum number of minimum dominating sets\, minimum total dominating sets\, and maximum independent sets» DTSTART;VALUE=DATE-TIME:20180906T080000Z DTEND;VALUE=DATE-TIME:20180906T090000Z DTSTAMP;VALUE=DATE-TIME:20180831T083011Z UID:f3db90d9-aed7-46cd-ad12-23f845748568 SEQUENCE:2 CREATED;VALUE=DATE-TIME:20180831T083011Z DESCRIPTION:We consider the stated numbers mainly in trees\, forests\, and connected graphs. Among others we give a very simple proof of Zykov's gen eralization of Turán's theorem\, and verify a conjecture of Derikvand and Oboudi. \n\nThe presented results are joint work with J. Alvarado\, S. Da ntas\, M.A. Henning\, and E. Mohr. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/f3db90d9-aed7-46cd-ad12-23f845748568 END:VEVENT BEGIN:VEVENT SUMMARY:Kolja Knauer\, «Generating k-connected orientations» DTSTART;VALUE=DATE-TIME:20190606T080000Z DTEND;VALUE=DATE-TIME:20190606T090000Z DTSTAMP;VALUE=DATE-TIME:20190603T204109Z UID:8874defd-e4b3-4aa1-8d37-f351e2b98833 SEQUENCE:0 CREATED;VALUE=DATE-TIME:20190603T204109Z DESCRIPTION:We present a simple algorithm\, that given a graph G generates \nall of its k-arc-connected orientations. Its amortized runtime is\nbasic ally the same as the one of an algorithm that can be extracted from the th eory of submodular flows. The latter is however rather intricate.\n\nAnoth er nice thing is\, that our algorithm actually consists of two\nmodules of independent interest:\n1. an algorithm that generates all orientations of G with prescribed\noutdegree sequence\,\n2. an algorithm that generates a ll outdegree sequences of k-connected orientations of G.\n\nJoint work wit h Sarah Blind and Petru Valicov LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/8874defd-e4b3-4aa1-8d37-f351e2b98833 END:VEVENT BEGIN:VEVENT SUMMARY:Sebastian Wiederracht\, «The Flat Wall Theorem for Bipartite Grap hs with Perfect Matchings» DTSTART;VALUE=DATE-TIME:20211007T080000Z DTEND;VALUE=DATE-TIME:20211007T090000Z DTSTAMP;VALUE=DATE-TIME:20210901T130539Z UID:9dc58661-74fe-41e0-961b-686f7304c8ff SEQUENCE:6 CREATED;VALUE=DATE-TIME:20210901T130539Z DESCRIPTION:Matching minors are a specialized version of minors fit for th e study of graphs with perfect matchings. The first major appearance of ma tching minors was in a result by Little who showed that a bipartite graph is Pfaffian if and only if it does not contain $K_{3\,3\,}$ as a matching minor. Later it was shown\, that $K_{3\,3\,}$-matching minor free bipartit e graphs are\, apart from a single exception\, essentially bipartite plana r graphs glued together at 4-cycles. We generalize these ideas by giving a n approximate description of bipartite graphs excluding $K_{t\,t}$ as a ma tching minor in the spirit of the famous Flat Wall Theorem of Robertson an d Seymour. In essence\, we show that every bipartite $K_{t\,t}$-matching m inor free graph is locally $K_{3\,3}$-matching minor free after removing a n apex set of bounded size. LAST-MODIFIED;VALUE=DATE-TIME:20211123T084225Z LOCATION:BAT4 l Séminaire LIRMM - RDC Entrée et https://bbb.lirmm.fr/b/d im-ajj-ddd URL:https://info-web.lirmm.fr/collorg/9dc58661-74fe-41e0-961b-686f7304c8ff END:VEVENT BEGIN:VEVENT SUMMARY:Claire Pennarun\, «Power domination on triangular grids with tria ngular and hexagonal shape» DTSTART;VALUE=DATE-TIME:20180125T090000Z DTEND;VALUE=DATE-TIME:20180125T100000Z DTSTAMP;VALUE=DATE-TIME:20180105T085200Z UID:2ea5fdae-351a-497c-9249-3aad682756ee SEQUENCE:2 CREATED;VALUE=DATE-TIME:20180105T085200Z DESCRIPTION:The concept of power domination emerged from the problem of mo nitoring electrical systems. Given a graph G and a set S \\subseteq V(G)\, a set M of monitored vertices is built as follows: at first\, M contains only the vertices of S and their direct neighbors\, and then each time a v ertex in M has exactly one neighbor not in M\, this neighbor is added to M .\nThe power domination number of a graph G is the minimum size of a set S such that this process ends up with the set M containing every vertex of G.\nWe here give some key ideas to the proofs of the exact power dominatio n number of triangular grids with hexagonal-shaped border\, and of triangu lar grids with triangular-shaped border. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/2ea5fdae-351a-497c-9249-3aad682756ee END:VEVENT BEGIN:VEVENT SUMMARY:Stephane Bessy\, «Out-colourings of digraphs.» DTSTART;VALUE=DATE-TIME:20171207T090000Z DTEND;VALUE=DATE-TIME:20171207T100000Z DTSTAMP;VALUE=DATE-TIME:20171102T145053Z UID:fa543bf9-f8e9-40d6-a204-8473aa7c2da4 SEQUENCE:2 CREATED;VALUE=DATE-TIME:20171102T145053Z DESCRIPTION:Joint work with N. Alon (Tel-Aviv U.) and J. Bang-Jensen (Sout h-Denmark U.).\n\nWe study vertex colourings of digraphs so that no out-ne ighbourhood is monochromatic and call such a colouring an out-colouring. T he problem of deciding whether a given digraph has an out-colouring with o nly two colours (called a 2-out-colouring) is NP-complete. We prove that\, except for the Paley tournament P7 \, every semicomplete digraph of minim um out-degree at\nleast 3 has a 2-out-colouring. Furthermore we consider the generalization of 2-out-colourings to vertex partitions (V1 \, V2) of a digraph D so that each of the three digraphs induced by respectively\, t he vertices of V1 \, the vertices of V2 and all arcs between V1 and V2 hav e minimum out-degree k for a prescribed integer k ≥ 1. Using probabilist ic arguments we prove that there exists an absolute constant c so that eve ry semicomplete digraph of minimum out-degree at least 2k + c.sqrt(k) has such a partition. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/fa543bf9-f8e9-40d6-a204-8473aa7c2da4 END:VEVENT BEGIN:VEVENT SUMMARY:Matthieu Rosenfeld\, «Bounding the number of sets defined by a gi ven MSO formula on trees» DTSTART;VALUE=DATE-TIME:20210708T080000Z DTEND;VALUE=DATE-TIME:20210708T090000Z DTSTAMP;VALUE=DATE-TIME:20210521T091516Z UID:8ac4fe4a-9938-4cb4-9243-41d08f778e67 SEQUENCE:2 CREATED;VALUE=DATE-TIME:20210521T091516Z DESCRIPTION:Monadic second-order logic can be used to express many classic al notions of sets of vertices of a graph as for instance: dominating sets \, induced matchings\, perfect codes\, independent sets\, or irredundant s ets. Bounds on the number of sets of any such family of sets are interesti ng from a combinatorial point of view and have algorithmic applications. M any such bounds on different families of sets over different classes of gr aphs are already provided in the literature. In particular\, Rote recently showed that the number of minimal dominating sets in trees of order n is at most 95^(n/13) and that this bound is asymptotically sharp up to a mult iplicative constant. We build on his work to show that what he did with mi nimal dominating sets can be done with any family of sets definable by a m onadic second-order formula. LAST-MODIFIED;VALUE=DATE-TIME:20210707T080102Z LOCATION:https://bbb.lirmm.fr/b/dim-ajj-ddd URL:https://info-web.lirmm.fr/collorg/8ac4fe4a-9938-4cb4-9243-41d08f778e67 END:VEVENT BEGIN:VEVENT SUMMARY:Dimitrios Thilikos\, «Structure and Enumeration of K4-free links and link diagrams» DTSTART;VALUE=DATE-TIME:20180705T080000Z DTEND;VALUE=DATE-TIME:20180705T090000Z DTSTAMP;VALUE=DATE-TIME:20180629T131703Z UID:722a3c75-ff23-400e-9458-89a072aa74b2 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20180629T131703Z DESCRIPTION:We study the class L of link types that admit a K4-minor-free diagram\, i.e.\, they can be projected on the plane so that the resulting graph does not contain any subdivision of K4. We prove that L is the closu re of a subclass of torus links under the operation of connected sum. Usin g this structural result\, we enumerate L and subclasses of it\, with resp ect to the minimal number of crossings or edges in a projection of L ∈ L . Further\, we enumerate (both exactly and asymptotically) all connected K 4-minor-free link diagrams\, all minimal connected K4-minor-free link diag rams\, and all K4-minor-free diagrams of the unknot. \n\nJoint work with J. Rué and V. Velona LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/722a3c75-ff23-400e-9458-89a072aa74b2 END:VEVENT BEGIN:VEVENT SUMMARY:Journée Gotha\, ANR Robust\, «GoTHA workshop on robust schedulin g» DTSTART;VALUE=DATE-TIME:20170427T070000Z DTEND;VALUE=DATE-TIME:20170427T150000Z DTSTAMP;VALUE=DATE-TIME:20170405T101030Z UID:9a93c025-2d16-47a2-82c5-e58039c207ae SEQUENCE:1 CREATED;VALUE=DATE-TIME:20170405T101030Z DESCRIPTION:Voir \nhttps://www.lirmm.fr/users/utilisateurs-lirmm/michael-p oss/gotha-workshop-on-robust-scheduling LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:bat 5 salle 1/124 URL:https://info-web.lirmm.fr/collorg/9a93c025-2d16-47a2-82c5-e58039c207ae END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Bellitto\, «Connectivity and routing in forbidden-transiti on graphs» DTSTART;VALUE=DATE-TIME:20210204T090000Z DTEND;VALUE=DATE-TIME:20210204T100000Z DTSTAMP;VALUE=DATE-TIME:20210108T104253Z UID:90fd0e73-0589-458b-a98f-685b2658c325 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20210108T104253Z DESCRIPTION:Graphs have proved to be an extremely useful tool to model rou ting problems in a very wide range of applications. However\, in some of t hem\, we sometimes need to express constraints on the permitted walks that are stronger than what the standard graph model allows for. For example\, in a road network\, there can be a crossroad where drivers are not allowe d to turn right and in this case\, many walks in the underlying graph woul d correspond to routes that a driver is not allowed to use. To overcome th is limitation\, Kotzig introduced the stronger model of forbidden-transiti on graphs. A transition is a pair of adjacent edges (or consecutive arcs i n the directed case) and a forbidden-transition graph is therefore a graph defined together with a set of pairs of adjacent edges that one may not u se consecutively.\nBecause of their expressiveness and practical interest\ , the study of forbidden-transition graphs is a fast-emerging field but we are still very far from understanding them as well as regular graphs. Pro blems of routing\, connectivity or robustness in those graphs have receive d growing attention in the last few decades but unfortunately\, those prob lems generally turn out to be algorithmically very difficult\, even on res tricted subclasses of graphs.\nIn this talk\, I will give an introduction to forbidden-transition graphs\, present some important variants\, some of the challenges that their study raises and discuss a few applications. I will present results I obtained with Benjamin Bergougnoux\, Jørgen Bang-J ensen and Anders Yeo on minimum connectivity requirements. Finally\, I wil l present an ongoing project that studies the parametrized complexity of i mportant difficult problems in these graphs. LAST-MODIFIED;VALUE=DATE-TIME:20210203T090102Z LOCATION:Téléseminaire: https://bbb.lirmm.fr/b/dim-ajj-ddd URL:https://info-web.lirmm.fr/collorg/90fd0e73-0589-458b-a98f-685b2658c325 END:VEVENT BEGIN:VEVENT SUMMARY:Lucia Penso\, «Dynamic monopolies and Vaccination» DTSTART;VALUE=DATE-TIME:20180920T080000Z DTEND;VALUE=DATE-TIME:20180920T090000Z DTSTAMP;VALUE=DATE-TIME:20180831T083049Z UID:5ccb359a-a5b8-4efa-9650-8041f7166ea5 SEQUENCE:3 CREATED;VALUE=DATE-TIME:20180831T083049Z DESCRIPTION:TBA LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/5ccb359a-a5b8-4efa-9650-8041f7166ea5 END:VEVENT BEGIN:VEVENT SUMMARY:Claire Pennarun\, «Compter les orientations eulériennes» DTSTART;VALUE=DATE-TIME:20170420T080000Z DTEND;VALUE=DATE-TIME:20170420T090000Z DTSTAMP;VALUE=DATE-TIME:20170407T151123Z UID:0d6a2c81-6ccc-4313-b951-fc04ae89fca6 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20170407T151123Z DESCRIPTION:Nous commencerons par détailler la construction classique des cartes Eulériennes planaires et par proposer une variante de cette const ruction.\nLes cartes Eulériennes planaires sont des objets combinatoires bien connus et leur nombre a une expression simple.\nSi maintenant on veut orienter ces cartes de manière "Eulérienne"\, c'est-à-dire que pour to ut sommet\, les degrés entrant et sortant sont égaux\, alors on obtient la famille des orientations eulériennes planaires (PEO). Nous allons voir pourquoi les décompositions classiques ne permettent pas de trouver dire ctement la série génératrice des PEO. Nous montrerons comment "contourn er" ce problème en définissant des sur- et sous-familles des PEO\, qui e lles possèdent des séries génératrices calculables et même algébriqu es. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION: URL:https://info-web.lirmm.fr/collorg/0d6a2c81-6ccc-4313-b951-fc04ae89fca6 END:VEVENT BEGIN:VEVENT SUMMARY:Remy Belmonte\, «Recent Results on the Complexity of Defective Co loring» DTSTART;VALUE=DATE-TIME:20180607T080000Z DTEND;VALUE=DATE-TIME:20180607T090000Z DTSTAMP;VALUE=DATE-TIME:20180504T122807Z UID:89a0abd6-19b3-4ae1-b523-ebdf2a29531a SEQUENCE:1 CREATED;VALUE=DATE-TIME:20180504T122807Z DESCRIPTION:In Defective Coloring we are given a graph G=(V\,E) and two in tegers \\chi_d\, \\Delta^∗ and are asked if we can partition V into \\ch i_d color classes\, so that each class induces a graph of maximum degree \ \Delta^∗. \n\nWe present two sets of recent results regarding the comple xity of the problem: first when the input graph is restricted to belong to some specific classes (split graphs\, cographs and trivially perfect grap hs in particular)\; second\, when the problem is parameterized by the tree width\, pathwidth\, tree-depth\, or feedback vertex set of the input graph .\n\nThis is a joint work with Michael Lampis and Valia Mitsou. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/89a0abd6-19b3-4ae1-b523-ebdf2a29531a END:VEVENT BEGIN:VEVENT SUMMARY:William Lochet\, «A proof of the Erd\\H{o}s-Sands-Sauer-Woodrow c onjecture.» DTSTART;VALUE=DATE-TIME:20170615T080000Z DTEND;VALUE=DATE-TIME:20170615T090000Z DTSTAMP;VALUE=DATE-TIME:20170412T160444Z UID:a8c878e1-546d-43c8-865d-6da271f14548 SEQUENCE:0 CREATED;VALUE=DATE-TIME:20170412T160444Z DESCRIPTION:A very nice result of B\\'ar\\'any and Lehel asserts that ever y finite subset $X$ or $\\mathbb R^d$ can be covered by $f(d)$ $X$-boxes ( i.e. each box has two antipodal points in $X$). As shown by Gy\\'arf\\'as and P\\'alv\\H{o}lgyi this result would follow from the following conjectu re : If a tournament admits a partition of its arc set into $k$ quasi orde rs\, then its domination number is bounded in terms of $k$. This question is in turn implied by the Erd\\H{o}s-Sands-Sauer-Woodrow conjecture : If t he arcs of a tournament $T$ are colored with $k$ colors\, there is a set $ X$ of at most $g(k)$ vertices such that for every vertex $v$ of $T$\, ther e is a monochromatic path from $X$ to $v$. We give a short proof of this s tatement. We moreover show that the general Sands-Sauer-Woodrow conjecture (which as a special case implies the stable marriage theorem) is valid fo r directed graphs with bounded stability number. This conjecture remains h owever open. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION: URL:https://info-web.lirmm.fr/collorg/a8c878e1-546d-43c8-865d-6da271f14548 END:VEVENT BEGIN:VEVENT SUMMARY:Rémy Belmonte\, «Token Sliding on Split Graphs» DTSTART;VALUE=DATE-TIME:20190321T090000Z DTEND;VALUE=DATE-TIME:20190321T100000Z DTSTAMP;VALUE=DATE-TIME:20190128T071902Z UID:5122642f-dd4a-4f8f-8b4d-8816c732391c SEQUENCE:2 CREATED;VALUE=DATE-TIME:20190128T071902Z DESCRIPTION:We consider the complexity of the Independent Set\nReconfigura tion problem under the Token Sliding rule. In this problem we are\ngiven t wo independent sets of a graph and are asked if we can transform one to th e other by repeatedly exchanging a vertex that is currently in the set wit h\none of its neighbors\, while maintaining the set independent. Our main result is\nto show that this problem is PSPACE-complete on split graphs (a nd hence also on chordal graphs)\, thus resolving an open problem in this area. We then\ngo on to consider the $c$-Colorable Reconfiguration problem \nunder the same rule\, where the constraint is now to maintain the set\n$ c$-colorable at all times.\n\nJoint work with Eun-Jung Kim\, Michael Lampi s\, Valia Mitsou\, Yota\nOtachi and Florian Sikora. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/5122642f-dd4a-4f8f-8b4d-8816c732391c END:VEVENT BEGIN:VEVENT SUMMARY:Jean-Florent Raymond\, «Packing and covering immersion models of planar subcubic graphs» DTSTART;VALUE=DATE-TIME:20160414T080000Z DTEND;VALUE=DATE-TIME:20160414T093000Z DTSTAMP;VALUE=DATE-TIME:20160330T123020Z UID:996163eb-6a0e-470e-b494-94fa7884e057 SEQUENCE:0 CREATED;VALUE=DATE-TIME:20160330T123020Z DESCRIPTION:A graph H is an immersion of a graph G if H can be obtained by lifting incident edges of some subgraph of G. We prove that there is a po lynomial function f:N×N→N\, such that if H is a connected planar subcub ic graph on h>0 edges\, G is a graph\, and k is a non-negative integer\, t hen either G contains k vertex/edge-disjoint subgraphs\, each containing H as an immersion\, or G contains a set F of f(k\,h) vertices/edges such th at G∖F does not contain H as an immersion.\n\nThis is join work with Arc hontia Giannopoulou (University of Warsaw)\, O-joung Kwon (Hungarian Acade my of Sciences) and Dimitrios M. Thilikos (LIRMM). A preprint is online: h ttp://arxiv.org/abs/1602.04042 . LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/996163eb-6a0e-470e-b494-94fa7884e057 END:VEVENT BEGIN:VEVENT SUMMARY:William Lochet\, «EPTAS for k-means Clustering of Affine Subspace s» DTSTART;VALUE=DATE-TIME:20210909T080000Z DTEND;VALUE=DATE-TIME:20210909T090000Z DTSTAMP;VALUE=DATE-TIME:20210823T122207Z UID:28176e4c-f5bb-491b-a0fd-ff8a7d3cf479 SEQUENCE:2 CREATED;VALUE=DATE-TIME:20210823T122207Z DESCRIPTION:Clustering is one of the most widely used techniques in data m ining\, statistics\, and machine learning. In general\, the purpose of clu stering is to group a set of objects such that similar objects end up in t he same cluster. A common approach to clustering is to treat objects with $d$ features as points in $\\mathbb{R}^d$ and the measure of the similarit y between two objects is the Euclidian distance between the corresponding points. One of the most famous mathematical models of data clustering is $k$-means. In $k$-means clustering\, we want to partition the points in $\ \mathbb{R}^d$\, or some other metric space\, by selecting a set of $k$ cen ters and assign each of the points to its closest center. The quality of t he clustering solution is characterized by the $k$-means cost function\, w hich minimizes the sum of squared distances between every point and its ne arest center. Here we consider a generalization of $k$-means clustering fo r data with incomplete or corrupted entries. When data objects are represe nted by points in $\\mathbb{R}^d$\, a data point is said to be incomplete when some of its entries are missing or unspecified. An incomplete data po int with at most $\\Delta$ unspecified entries corresponds to an axis-para llel affine subspace of dimension at most $\\Delta$\, called a $\\Delta$-p oint. Thus we seek a partition of $n$ input $\\Delta$-points into $k$ clus ters minimizing the $k$-means objective. For $\\Delta=0$\, when all coordi nates of each point are specified\, this is the usual $k$-means clustering . We give an algorithm that finds an $(1+\\epsilon)$-approximate solution in time $f(k\,\\epsilon\, \\Delta) \\cdot n^2 \\cdot d$ for some function $f$ of $k\,\\epsilon$\, and $\\Delta$ only. Our algorithm is a generalizat ion of Kumar et al. algorithm for the usual $k$-means clustering and a lar ge part of the talk will be spent explaining that algorithm.\n\nThis is jo int work with E. Eiben\, F. Fomin\, P. Golovach\, F. Panolan\, and K. Simo nov \n\nThe paper can be found https://arxiv.org/abs/2010.09580 LAST-MODIFIED;VALUE=DATE-TIME:20210910T075710Z LOCATION:https://bbb.lirmm.fr/b/dim-ajj-ddd et C. BAT4-E3.23 Etage-Extensi on URL:https://info-web.lirmm.fr/collorg/28176e4c-f5bb-491b-a0fd-ff8a7d3cf479 END:VEVENT BEGIN:VEVENT SUMMARY:speaker\, «title» DTSTART;VALUE=DATE-TIME:20100413T220000Z DTEND;VALUE=DATE-TIME:20100413T220000Z DTSTAMP;VALUE=DATE-TIME:20170330T151848Z UID:db52c6c6-bbe4-43cb-9df6-ff811c11d818 SEQUENCE:10 CREATED;VALUE=DATE-TIME:20170330T151848Z DESCRIPTION:text LAST-MODIFIED;VALUE=DATE-TIME:20171016T141136Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/db52c6c6-bbe4-43cb-9df6-ff811c11d818 END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Gonçalves\, «Dushnik-Miller dimension of contact systems of d-dimensional boxes» DTSTART;VALUE=DATE-TIME:20180322T093000Z DTEND;VALUE=DATE-TIME:20180322T103000Z DTSTAMP;VALUE=DATE-TIME:20180202T091725Z UID:a408fcfb-3a53-4b34-a4cb-891a1967e0f1 SEQUENCE:4 CREATED;VALUE=DATE-TIME:20180202T091725Z DESCRIPTION:Planar graphs are the graphs with Dushnik-Miller dimension at most three (W. Schnyder\, Planar graphs and poset dimension\, Order 5\, 32 3-343\, 1989). Consider the intersection graph of interior disjoint axis-p arallel rectangles in the plane. It is known that if at most three rectang les intersect on a point\, then this intersection graph is planar\, that i s it has Dushnik-Miller dimension at most three. During this talk we will this result\, from the plane to $R^d$\, by considering tilings of $R^d$ wi th axis parallel boxes\, where at most $d+1$ boxes intersect on a point. S uch tilings induce simplicial complexes and we will show that those simpli cial complexes have Dushnik-Miller dimension at most $d+1$. This is a join t work with M.C. Francis. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/a408fcfb-3a53-4b34-a4cb-891a1967e0f1 END:VEVENT BEGIN:VEVENT SUMMARY:Vasiliki Velona\, «Learning partial correlation graphs and graphi cal models by covariance queries» DTSTART;VALUE=DATE-TIME:20210923T080000Z DTEND;VALUE=DATE-TIME:20210923T090000Z DTSTAMP;VALUE=DATE-TIME:20210825T111901Z UID:b73a631b-3bed-48f8-aaed-9c8b7396fca4 SEQUENCE:4 CREATED;VALUE=DATE-TIME:20210825T111901Z DESCRIPTION:We study the problem of recovering the structure underlying la rge Gaussian graphical models or\, more generally\, partial correlation gr aphs. In high-dimensional problems\, it is often too costly to store the e ntire sample covariance matrix. We propose a new input model in which one can query single entries of the covariance matrix. We prove that it is pos sible to recover the support of the inverse covariance matrix with low que ry and computational complexity. Our algorithms work in a regime when this support is represented by tree-like graphs and\, more generally\, for gra phs of small treewidth. Our results demonstrate that for large classes of graphs\, the structure of the corresponding partial correlation graphs can be determined much faster than even computing the empirical covariance ma trix. \n\nThe results of the talk are joint work with Gábor Lugosi\, Jaku b Truszkowski\, and Piotr Zwiernik. LAST-MODIFIED;VALUE=DATE-TIME:20210922T080103Z LOCATION:BAT4 l Séminaire LIRMM - RDC Entrée et https://bbb.lirmm.fr/b/d im-ajj-ddd URL:https://info-web.lirmm.fr/collorg/b73a631b-3bed-48f8-aaed-9c8b7396fca4 END:VEVENT BEGIN:VEVENT SUMMARY:Raul Lopes\, «Disjoint paths\, grids and tree-width: the directed case.» DTSTART;VALUE=DATE-TIME:20181025T080000Z DTEND;VALUE=DATE-TIME:20181025T090000Z DTSTAMP;VALUE=DATE-TIME:20180831T073057Z UID:19eb6c83-307d-4ec9-815d-ebd9655967af SEQUENCE:4 CREATED;VALUE=DATE-TIME:20180831T073057Z DESCRIPTION:Width parameters in graphs can be seen as an estimation to how similar a graph is a to a typical structure. Graphs with bounded width pa rameters are usually decomposed into small parts\, which in turn are place d under a set of rules and relations between them. Therefore\, we can make use of classical algorithm construction techniques exploring those proper ties\, like dynnamic programming\, to efficiently solve many hard problems in graphs with bounded width parameters.\n\nThe focus of this work is on tree-width for directed graphs. This parameter is used to estimate how clo se a directed graph is to a directed acyclic graph. In particular\, we sho w a parameterized algorithm\, under parameter k\, which either finds a dir ected tree decomposition of width at most 3k-2 or generates a certificate that the width of the given graph is at least k-1. We hope to apply this r esult as a first step to show that the recent Directed Grid Theorem\, a re sult analogous to the Grid Theorem for directed graphs\, can be done in FP T time. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/19eb6c83-307d-4ec9-815d-ebd9655967af END:VEVENT BEGIN:VEVENT SUMMARY:Christophe Paul\, «A linear fixed parameter tractable algorithm f or connected pathwidth» DTSTART;VALUE=DATE-TIME:20200528T090000Z DTEND;VALUE=DATE-TIME:20200528T100000Z DTSTAMP;VALUE=DATE-TIME:20200507T132720Z UID:7013dd0c-50ef-4d53-8853-3af755b5089a SEQUENCE:7 CREATED;VALUE=DATE-TIME:20200507T132720Z DESCRIPTION:The graph parameter of //pathwidth// can be seen as a measure of the topological resemblance of a graph to a path. A popular definition of pathwidth is given in terms of //node search// where we are given a sy stem of tunnels (represented by a graph) that is contaminated by some inf ectious substance and we are looking for a search strategy that\, at each step\, either places a searcher on a vertex or removes a searcher from a vertex and where an edge is cleaned when both endpoints are simultaneousl y occupied by searchers. It was proved that the minimum number of searcher s required for a successful cleaning strategy is equal to the pathwidth of the graph plus one. Two desired characteristics for a cleaning strategy is to be //monotone// (no recontamination occurs) and //connected// (clean territories always remain connected). Under these two demands\, the numbe r of searchers is equivalent to a variant of pathwidth called //connected pathwidth//. We prove that connected pathwidth is fixed parameter tractab le\, in particular we design a $2^{O(k^2)}\\cdot n$ time algorithm that ch ecks whether the connected pathwidth of $G$ is at most $k.$ This resolves an open question by [//Dereniowski\, Osula\, and Rzążewski\, Finding sma ll-width connected path-decompositions in polynomial time. Theor. Comput. Sci.\, 794:85–100\, 2019}//]. For our algorithm\, we enrich the //typica l sequence technique// that is able to deal with the connectivity demand. Typical sequences have been introduced in [//Bodlaender and Kloks. Effici ent and constructive algorithms for the pathwidth and treewidth of graphs. J. Algorithms\, 21(2):358–402\, 1996}//] for the design of linear param eterized algorithms for treewidth and pathwidth. While this technique has been later applied to other parameters\, none of its advancements was ab le to deal with the connectivity demand\, as it is a «global» demand tha t concerns an unbounded number of parts of the graph of unbounded size. Th e proposed extension is based on an encoding of the connectivity propert y that is quite versatile and may be adapted so to deliver linear parame terized algorithms for the connected variants of other width parameters as well. An immediate consequence of our result is a $2^{O(k^2)}\\cdot n$ ti me algorithm for the monotone and connected version of the edge search num ber.\n\nJoint work with Mamadou Moustapha Kanté and Dimitrios M. Thilikos \n\nhttps://moodle.umontpellier.fr/course/view.php?id=15640 LAST-MODIFIED;VALUE=DATE-TIME:20200527T090103Z LOCATION:Téléseminaire URL:https://info-web.lirmm.fr/collorg/7013dd0c-50ef-4d53-8853-3af755b5089a END:VEVENT BEGIN:VEVENT SUMMARY:Jocelyn Thiebaut\, «Packing arc-disjoint cycles and triangles in tournaments» DTSTART;VALUE=DATE-TIME:20180517T080000Z DTEND;VALUE=DATE-TIME:20180517T090000Z DTSTAMP;VALUE=DATE-TIME:20180323T130836Z UID:2519e94b-1bc9-4230-a601-81857cdd082e SEQUENCE:2 CREATED;VALUE=DATE-TIME:20180323T130836Z DESCRIPTION:A tournament is a directed graph in which there is a single ar c between every pair of distinct vertices. Tournaments form a mathematical ly rich subclass of directed graphs with interesting structural and algori thmic properties. \nGiven a tournament $T$ on $n$ vertices\, we explore th e problems of determining if $T$ has a cycle packing (a set of pairwise ar c-disjoint cycles) of size $k$ and a triangle packing (a set of pairwise a rc-disjoint triangles) of size $k$. We refer to these problems as ACT and ATT\, respectively. \nAlthough the maximization version of ACT can be see n as the linear programming dual of finding a minimum feedback arc set (a set of arcs whose deletion results in an acyclic graph) in tournaments whi ch has been widely studied\, surprisingly no algorithmic results seem to e xist concerning the former. \n\nIn this talk\, we explore the classical an d parameterized complexity of both ATT and ACT. In particular\, we focus o n the NP-completeness of ATT and we give a vertex-linear kernel for this p roblem. \n\nThis is joint work with S. Bessy\, M. Bougeret\, R. Krithika\, A. Sahu\, S. Saurabh and M. Zehavi. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/2519e94b-1bc9-4230-a601-81857cdd082e END:VEVENT BEGIN:VEVENT SUMMARY:Alexandre Vigny\, «Query enumeration and nowhere dense classes of graphs» DTSTART;VALUE=DATE-TIME:20210211T090000Z DTEND;VALUE=DATE-TIME:20210211T100000Z DTSTAMP;VALUE=DATE-TIME:20210111T085532Z UID:59b46a7e-f424-4c21-896e-cb9dd087df89 SEQUENCE:0 CREATED;VALUE=DATE-TIME:20210111T085532Z DESCRIPTION:Given a query q and a graph G the enumeration of q over G cons ists in computing\, one element at a time\, the set q(G) of all solutions to q on G. The delay is the maximal time between two consecutive output an d the preprocessing time is the time needed to produce the first solution. Ideally\, we would like to have constant delay enumeration after linear p reprocessing. Since this it is not always possible to achieve\, we need to add restriction to the classes of graphs and/or queries we consider.\n\nI n this talk I will talk about some restrictions for which such algorithms exist: graphs with bounded degree\, tree-like structures\, conjunctive que ries...\nWe will more specifically consider nowhere dense classes of graph s: What are they? Why is this notion relevant? How to make algorithms from these graph properties? LAST-MODIFIED;VALUE=DATE-TIME:20210210T090102Z LOCATION:Téléseminaire: https://bbb.lirmm.fr/b/dim-ajj-ddd URL:https://info-web.lirmm.fr/collorg/59b46a7e-f424-4c21-896e-cb9dd087df89 END:VEVENT BEGIN:VEVENT SUMMARY:Ignasi Sau\, «On the complexity of finding large odd induced subg raphs and odd colorings» DTSTART;VALUE=DATE-TIME:20200618T090000Z DTEND;VALUE=DATE-TIME:20200618T100000Z DTSTAMP;VALUE=DATE-TIME:20200507T125313Z UID:8870670b-0a85-417e-a26a-a66b5068417c SEQUENCE:12 CREATED;VALUE=DATE-TIME:20200507T125313Z DESCRIPTION:This talk is about the problems of finding\, given a graph $G$ \, a largest induced subgraph of $G$ with all degrees odd (called an \\emp h{odd} subgraph)\, and the smallest number of odd subgraphs that partition $V(G)$. We call these parameters $mos(G)$ and $\\chi_{odd}(G)$\, respecti vely. We will discuss (some of) the following results: \n\n- Deciding whet her $\\chi_{odd}(G) \\leq q$ is polynomial-time solvable if $q \\leq 2$\, and NP-complete otherwise. \n- FPT algorithms in time $2^{O(rw)}poly(n)$ a nd $2^{O(q \\cdot rw)}poly(n)$ to compute $mos(G)$ and to decide whether $ \\chi_{odd}(G) \\leq q$ on an $n$-vertex graph $G$ of rank-width at most $ rw$\, respectively. The dependency on rank-width is asymptotically optimal under the ETH. \n- Some tight bounds for these parameters on restricted g raph classes or in relation to other parameters.\n\nJoint work with Rémy Belmonte\n\n\nhttp://bbb.lirmm.fr/b/dim-ajj-ddd LAST-MODIFIED;VALUE=DATE-TIME:20200617T090103Z LOCATION:Téléseminaire URL:https://info-web.lirmm.fr/collorg/8870670b-0a85-417e-a26a-a66b5068417c END:VEVENT BEGIN:VEVENT SUMMARY:Petr Golovach\, «Parameterized Enumeration Kernels with Applicat ions to Matching Cut Enumeration» DTSTART;VALUE=DATE-TIME:20201203T090000Z DTEND;VALUE=DATE-TIME:20201203T090000Z DTSTAMP;VALUE=DATE-TIME:20201126T132734Z UID:1b70ef8b-1f53-4947-9eb4-d09c92925db9 SEQUENCE:6 CREATED;VALUE=DATE-TIME:20201126T132734Z DESCRIPTION:An enumeration kernel as defined by Creignou et al. [Theory Co mput. Syst. 2017] for a parameterized enumeration problem consists of an a lgorithm that transforms each instance into one whose size is bounded by t he parameter plus a solution-lifting algorithm that efficiently enumerates all solutions from the set of the solutions of the kernel. We propose to consider two new versions of enumeration kernels by asking that the soluti ons of the original instance can be enumerated in polynomial time or with polynomial delay from the kernel solutions. Using the NP-hard Matching Cut problem parameterized by structural parameters such as the vertex cover n umber or the cyclomatic number of the input graph\, we show that the new e numeration kernels present a useful notion of data reduction for enumerati on problems which allows to compactly represent the set of feasible soluti ons.\n\njoint work with Christian Komusiewicz\, Dieter Kratsch\, and Van Bang Le\n\n\nTéléseminaire: [[https://bbb.lirmm.fr/b/dim-ajj-ddd]] LAST-MODIFIED;VALUE=DATE-TIME:20201202T090103Z LOCATION:Téléseminaire: https://bbb.lirmm.fr/b/dim-ajj-ddd URL:https://info-web.lirmm.fr/collorg/1b70ef8b-1f53-4947-9eb4-d09c92925db9 END:VEVENT BEGIN:VEVENT SUMMARY:Pascal Ochem\, «Homomorphism of planar signed graphs to unbalance d cycles.» DTSTART;VALUE=DATE-TIME:20180405T080000Z DTEND;VALUE=DATE-TIME:20180405T090000Z DTSTAMP;VALUE=DATE-TIME:20180316T092147Z UID:415fc816-04ab-41d9-9c21-7d5c6b3365c5 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20180316T092147Z DESCRIPTION:I will recall the definition of homomorphisms of signed graphs .\nFor k >= 1\, the unbalanced cycle UC_{2k} contains exactly one negative edge. I will show that for k >= 1\, deciding a planar signed graph has a homomorphism to UC_{2k} is NP-complete.\nThe proof needs the fact that the classical homomorphism of planar simple graphs to a cicrcular clique with degree 3 is NP-complete\, which is of independent interest. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/415fc816-04ab-41d9-9c21-7d5c6b3365c5 END:VEVENT BEGIN:VEVENT SUMMARY:Marin Bougeret\, «Tutoriel : comment obtenir des résultats d'ina pproximabilité pour son problème d'optimisation favori (ou plutôt\, com ment ignorer les nombreux outils de la théorie structurelle de l'approxim ation).» DTSTART;VALUE=DATE-TIME:20161006T080000Z DTEND;VALUE=DATE-TIME:20161006T084500Z DTSTAMP;VALUE=DATE-TIME:20161004T132253Z UID:8831b763-26f8-4fb5-9616-6da60017e14d SEQUENCE:0 CREATED;VALUE=DATE-TIME:20161004T132253Z DESCRIPTION:Dans cet exposé on fait un tour d'horizon rapide sur les outi ls existants pour prouver des résultats d'inapproximabilité. On a d'un c ôté les gap réductions\, l'outil "idéal" puisque sa définition est tr ès naturelle et qu'il permet d'obtenir des résultats forts. En effet\, l es nombreux résultats existants fournissent un large catalogue de problè mes pour lesquels \ndes résultats optimaux d'inapproximabilité sont conn us. On peut alors souvent réutiliser ces résultats (en écrivant des gap s réductions depuis ces problèmes)\, et déduire ainsi des résultats d' inapproximabilité forts pour son problème cible. Nous ne parlerons donc *pas* des gaps réductions\, \npuisque la littérature correspondante est abondante et facile à appréhender.\n\nD'un autre côté on trouve les "a pproximation preserving reductions". La difficulté est que derrière cett e expression se cache un ensemble important de réductions (strict\, S\, L \, E\, A\, AP\, PTAS ..)\, et qu'il est donc difficile à première vue de choisir quelle réduction utiliser (en plus du problème source à choisi r!). Cependant\, il se trouve que certaines de ces réductions ont été i ntroduites dans le cadre de la complexité structurelle\, c'est à dire po ur montrer qu'un problème\, parfois artificiellement construit\, est comp let pour une certaine classe. Ainsi\, en pratique (typiquement lorsque l'o n cherche à montrer qu'un problème n'admet pas de PTAS)\, il *semble* qu e beaucoup de ces réductions ne soient pas utilisées\, et que l'on cherc he simplement à construire une réduction vérifiant une certaine conditi on suffisante plus naturelle que les définitions des réductions précéd entes. \n\nNous parlerons de ces conditions suffisantes\, et illustrerons à travers les preuves (simples) des résultats suivants :\n- Vertex Cover n'admet pas de PTAS sur les graphes de degré maximum 3 (à moins que P=N P)\n- MAX CUT n'admet pas de PTAS (à moins que P=NP)\n- MAX 3SAT(B) (où chaque variable n'apparaît que dans au plus $B$ clauses) n'admet pas de P TAS (à moins que P=NP)\n\nNb : cet exposé n'est pas un exposé de recher che\, et le niveau technique se veut faible.\nDurée prévue : entre 30 et 45 min LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/8831b763-26f8-4fb5-9616-6da60017e14d END:VEVENT BEGIN:VEVENT SUMMARY:Eunjung kim\, «A polynomial kernel for Distance-Hereditary Vertex Deletion» DTSTART;VALUE=DATE-TIME:20170309T090000Z DTEND;VALUE=DATE-TIME:20170309T100000Z DTSTAMP;VALUE=DATE-TIME:20170225T081553Z UID:2319a1fa-234c-4935-8f26-ac04a9402535 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20170225T081553Z DESCRIPTION:A graph is distance-hereditary if for any pair of vertices\, t heir distance in every connected induced subgraph containing both ver- tic es is the same as their distance in the original graph. The Distance- Here ditary Vertex Deletion problem asks\, given a graph G on n vertices and an integer k\, whether there is a set S of at most k vertices in G such that G − S is distance-hereditary. This problem is impor- tant due to its co nnection to the graph parameter rank-width\; distance- hereditary graphs a re exactly graphs of rank-width at most 1. Eiben\, Ganian\, and Kwon (MFCS ’ 16) proved that Distance-Hereditary Ver- tex Deletion can be solved in time 2O(k)nO(1)\, and asked whether it admits a polynomial kernelization. We show that this problem admits a polynomial kernel\, answering this que stion positively. For this\, we use a similar idea for obtaining an approx imate solution for Chordal Ver- tex Deletion due to Jansen and Pilipczuk ( SODA’ 17) to obtain an approximate solution with O(k3 log n) vertices wh en the problem is a Yes-instance\, and we exploit the structure of split d ecompositions of distance-hereditary graphs to reduce the total size. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/2319a1fa-234c-4935-8f26-ac04a9402535 END:VEVENT BEGIN:VEVENT SUMMARY:Victor A. Campos\, «Free Lula Trees» DTSTART;VALUE=DATE-TIME:20181122T090000Z DTEND;VALUE=DATE-TIME:20181122T100000Z DTSTAMP;VALUE=DATE-TIME:20180926T092051Z UID:72cc57ed-bcb1-4414-8828-fed6b05d8060 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20180926T092051Z DESCRIPTION:In this talk\, we introduce Free Lula Trees. Free Lula Trees a re balanced binary search trees based on Red-Black Trees that can implemen t the usual Search/Insert/Delete/Successor/Predecessor operations in O(log n) time. Although never published\, this data structure was developed in 2000 to implement efficient priority queues for branch-and-bound applicati ons. \n\nA Split Tree is a Data Structure that contains a set of nodes and can search for and delete a given node x and split itself into two split trees in O(1) amortized time\, one containing all nodes with key less than x and the other with all nodes with key greater than x. Split trees were studied by Demaine et. al. in 2009\, but few details were given on how to do it in the BST model of computation. We show how an implementation of Sp lit Trees can be made in the BST model of computation using Free Lula Tree s.\n\nTo motivate Split Trees\, we will spend some time presenting the Dyn amic Optimality Conjecture and its Geometric View to relate it to an inter esting problem in Graph Theory. The Geometric View of the Dynamic Optimali ty Conjecture is based on a work by Demaine et. al.\n\nThis talk will be a dapted for people who do not usually work with Data Structures.\n\nTree na ming: Luiz Inácio Lula da Silva is a political prisoner in Brasil since A pril 7th 2018. He was jailed without reasonable evidence to prevent him fr om running for the 2018 election. The authors would like to plant a tree i n solidarity for him\, but a physical tree would probably be cut down in t he current situation of political turmoil that Brazil lives in. Therefore\ , we will plant a symbolic theoretical tree which can resist such hatred. \n\nJoint work with Ricardo Corrêa (Universidade Federal Rural do Rio de Janeiro - UFRRJ). LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/72cc57ed-bcb1-4414-8828-fed6b05d8060 END:VEVENT BEGIN:VEVENT SUMMARY:Alantha Newman\, «Algorithms for dicoloring» DTSTART;VALUE=DATE-TIME:20250911T080000Z DTEND;VALUE=DATE-TIME:20250911T090000Z DTSTAMP;VALUE=DATE-TIME:20250724T073200Z UID:d7f213be-8576-4da6-aef2-3feeb26401de SEQUENCE:1 CREATED;VALUE=DATE-TIME:20250724T073200Z DESCRIPTION:A vertex coloring of a digraph is proper if each directed cycl e\nreceives at least two colors. The dichromatic number of a digraph D\ni s the minimum integer k such that D has a proper k-coloring.\nEquivalently \, it is the minimum k such that the vertex set of D can be\npartitioned i nto k acyclic sets. The problem of bounding the\ndichromatic number has b een well-studied from the perspective of graph\ntheory\, for example with respect to forbidden induced subgraphs.\nIn this talk\, we consider algori thmic and complexity aspects of\ncoloring tournaments and digraphs\, and s how how these are connected to\nsome of the recently studied problems and results in graph theory.\n\nBased on joint works with Parinya Charlermsook \, Harmender Gahlawat\,\nFelix Klingelhoefer and Chaoliang Tang. LAST-MODIFIED;VALUE=DATE-TIME:20250910T080103Z LOCATION: URL:https://info-web.lirmm.fr/collorg/d7f213be-8576-4da6-aef2-3feeb26401de END:VEVENT BEGIN:VEVENT SUMMARY:Pas de séminaire (GROW à Aussois)\, «TBA» DTSTART;VALUE=DATE-TIME:20151015T080000Z DTEND;VALUE=DATE-TIME:20151015T090000Z DTSTAMP;VALUE=DATE-TIME:20150923T082108Z UID:92856626-1650-43ab-9a8d-c085ef50a93e SEQUENCE:1 CREATED;VALUE=DATE-TIME:20150923T082108Z DESCRIPTION:TBA LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION: URL:https://info-web.lirmm.fr/collorg/92856626-1650-43ab-9a8d-c085ef50a93e END:VEVENT BEGIN:VEVENT SUMMARY:Fabien Jacques\, «Complexity of 3 + 1/m-coloring Pt-free graphs» DTSTART;VALUE=DATE-TIME:20210916T080000Z DTEND;VALUE=DATE-TIME:20210916T090000Z DTSTAMP;VALUE=DATE-TIME:20210901T130216Z UID:ddb50422-59f5-45e4-a9b8-eeca5ab7ff3d SEQUENCE:2 CREATED;VALUE=DATE-TIME:20210901T130216Z DESCRIPTION:The 4-coloring problem is NP-complete for $P_7$-free graphs wh ereas the 3-coloring problem can be solved in quasi-polynomial time on $P_ t$-free graphs for any fixed t. We consider circular coloring to locate pr ecisely the complexity gap between 3 and 4 colors: for every fixed integer m ≥ 2\, the 3 + 1/m-coloring problem is NP-complete on $P_30$-free\ngra phs. LAST-MODIFIED;VALUE=DATE-TIME:20211221T042204Z LOCATION:BAT4 l Séminaire LIRMM - RDC Entrée et https://bbb.lirmm.fr/b/ dim-ajj-ddd URL:https://info-web.lirmm.fr/collorg/ddb50422-59f5-45e4-a9b8-eeca5ab7ff3d END:VEVENT BEGIN:VEVENT SUMMARY:Guilherme Gomes\, «On the complexity of finding cuts of bounded d egree» DTSTART;VALUE=DATE-TIME:20190207T090000Z DTEND;VALUE=DATE-TIME:20190207T100000Z DTSTAMP;VALUE=DATE-TIME:20181220T152823Z UID:11d061d2-03bd-4827-8cf0-df757d1c8d05 SEQUENCE:3 CREATED;VALUE=DATE-TIME:20181220T152823Z DESCRIPTION:A matching cut is a partition of the vertices of a graph in tw o sets A and B such that each vertex has at most one neighbor on the other side of the cut. The Matching Cut problem asks whether or not a graph has a matching cut\, and has been intensively studied in the literature. In t his talk\, we introduce a natural generalization of this problem\, which w e call d-Cut: for a positive integer d\, a d-cut is a bipartition of the v ertices of a graph into two sets A and B such that each vertex has at most d neighbors across the cut. We generalize (and in some cases\, improve) a number of results for the Matching Cut problem. Namely\, we begin with a n NP-hardness reduction for d-Cut on (2d+2)-regular graphs and a polynomia l algorithm for graphs of maximum degree at most d+2. We then give FPT alg orithms when parameterizing by: the maximum number of edges crossing the c ut\, treewidth\, distance to cluster\, and distance to co-cluster\; in par ticular\, the treewidth algorithm improves upon the running time of the be st known algorithm for Matching Cut. Our main technical contribution is a polynomial kernel for d-Cut\, for every positive integer d\, parameterized by the distance to a cluster graph. We also rule out the existence of pol ynomial kernels when parameterizing simultaneously by the number of edges crossing the cut\, the treewidth\, and the maximum degree. We conclude wit h an exact exponential algorithm slightly faster than the naive brute forc e approach running in time O(2^n). \n\nJoint work with Ignasi Sau. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/11d061d2-03bd-4827-8cf0-df757d1c8d05 END:VEVENT BEGIN:VEVENT SUMMARY:Mohammed SENHAJI\, «Neighbour-distinguishing decompositions of gr aphs» DTSTART;VALUE=DATE-TIME:20181206T090000Z DTEND;VALUE=DATE-TIME:20181206T100000Z DTSTAMP;VALUE=DATE-TIME:20181121T151746Z UID:6d181aa1-e947-4ec9-a38c-8d87d052affa SEQUENCE:1 CREATED;VALUE=DATE-TIME:20181121T151746Z DESCRIPTION:The main question taht we explore was introduced by Karonski\, Luczak and\nThomason in [KLT04] : Can we weight the edges of a graph G \, with weights 1 \,2 \, and 3 \, such that any two of adjacent vertices of G are distinguished by the sum of their incident weights ? This question l ater becomes the famous 1-2-3 Conjecture.\n\nIn this presentation we explo re several variants of the 1-2-3 Conjecture\, and\ntheir links with locall y irregular decompositions. We are interested in both\noptimisation result s and algorithmic problems. We first introduce an equitable version of the neighbour-sum-distinguishing edge-weightings\, that is a variant where we require every edge weight to be used the same number of times up to a dif ference of 1. Then we explore an injective variant where each edge is assi gned a different weight\, which yields necessarily an equitable weighting. This gives us first general upper bounds on the equitable version. Moreov er\, the injective variant is also a local version of the well-known antim agic labelling. After that we explore how neighbour-sum-distinguishing wei ghtings behave if we require sums of neighbouring vertices to differ by at least 2 . Namely\, we present results on the smallest maximal weight need ed to construct such weightings for some classes of graphs\, and study som e algorithmic aspects of this problem. Due\nto the links between neighbour -sum-distinguishing edge weightings and locally irregular decompositions\, we also explore the locally irregular index of subcubic graphs\, along wi th other variants of the locally irregular decomposition problem. Finally\ , we present a more general work toward a general theory unifying neighbou r-sum-distinguishing edge-weightings and locally irregular decompositions. \n\nWe also present a 2 -player game version of neighbour-sum-distinguishi ng edge-weightings and exhibit sufficient conditions for each player to wi n the game.\n\nReferences\n[KLT04] M. Karonski\, T. Luczak\, and A. Thomas on. Edge weights and vertex\ncolours. Journal of Combinatorial Theory\, Se ries B \, 91(1):151-157\, 2004. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/6d181aa1-e947-4ec9-a38c-8d87d052affa END:VEVENT BEGIN:VEVENT SUMMARY:Fabien Jacques\, «Homomorphisms of planar (m\,n)-colored-mixed gr aphs to planar targets» DTSTART;VALUE=DATE-TIME:20201112T090000Z DTEND;VALUE=DATE-TIME:20201112T100000Z DTSTAMP;VALUE=DATE-TIME:20200910T143844Z UID:52fca533-8bbc-4964-982e-1e0d1856e41f SEQUENCE:9 CREATED;VALUE=DATE-TIME:20200910T143844Z DESCRIPTION:An (m\,n)-colored-mixed graph G=(V\,A\,\,1\,\,\,A\,\,2\,\,\, ⋯\,A\,\,m\,\,\,E\,\,1\,\,\,E\,\,2\,\,\,⋯\,E\,\,n\,\,) is a graph havin g m colors of arcs and n colors of edges. We do not allow two arcs or edge s to have the same endpoints. A homomorphism from an (m\,n)-colored-mixed graph G to another (m\,n)-colored-mixed graph H is a morphism φ:V(G)→V( H) such that each edge (resp. arc) of G is mapped to an edge (resp. arc) o f H of the same color (and orientation). An (m\,n)-colored-mixed graph T i s said to be P\,\,g\,\,^^(m\,n)^^-universal if every graph in P\,\,g\,\,^^ (m\,n)^^ (the planar (m\,n)-colored-mixed graphs with girth at least g) ad mits a homomorphism to T. We show that planar P\,\,g\,\,^^(m\,n)^^-univers al graphs do not exist for 2m+n≥3 (and any value of g) and find a minima l (in the number vertices) planar P\,\,g\,\,^^(m\,n)^^-universal graphs in the other cases.\n\n\n\n\nTéléseminaire: [[https://bbb.lirmm.fr/b/dim-a jj-ddd]] LAST-MODIFIED;VALUE=DATE-TIME:20201111T090103Z LOCATION:Téléseminaire: https://bbb.lirmm.fr/b/dim-ajj-ddd URL:https://info-web.lirmm.fr/collorg/52fca533-8bbc-4964-982e-1e0d1856e41f END:VEVENT BEGIN:VEVENT SUMMARY:Martin Milanič\, «Tree Decompositions with Bounded Independence Number» DTSTART;VALUE=DATE-TIME:20210930T080000Z DTEND;VALUE=DATE-TIME:20210930T080000Z DTSTAMP;VALUE=DATE-TIME:20210816T032509Z UID:86a39139-0cdb-419d-94f1-022269e7be0f SEQUENCE:4 CREATED;VALUE=DATE-TIME:20210816T032509Z DESCRIPTION:Which graphs admit a tree decomposition such that each bag ind uces a subgraph with bounded independence number? When available\, such a tree decomposition can be used to solve the //Maximum Weight Independent S et// (MWIS) problem in polynomial time. We consider six graph containment relations: the subgraph\, topological minor\, and minor relations\, as wel l as their induced variants\, and for each of them characterize the graphs $H$ for which any graph excluding $H$ with respect to the relation admits a tree decomposition with bounded independence number.\n\nAs our main res ult\, we obtain an infinite family of graph classes that admit polynomial- time algorithms for the MWIS problem. All but two of these graph classes f orm a proper generalization of the class of chordal graphs\, and hence thi s result is a significant strengthening of the polynomial-time solvability of the MWIS problem for the class of chordal graphs given by Frank in 197 6. Another consequence is that the MWIS problem is solvable in polynomial time in the class of $1$-perfectly orientable graphs\, answering a questio n of Beisegel\, Chudnovsky\, Gurvich\, Milanič\, and Servatius [WADS 2019 ].\n\n\nJoint work with Clément Dallard and Kenny Štorgel. LAST-MODIFIED;VALUE=DATE-TIME:20210929T080102Z LOCATION:https://bbb.lihttps://bbb.lirmm.fr/b/dim-ajj-ddd et C. BAT4-E3.23 Etage-Extension rmm.fr/b/dim-ajj-ddd URL:https://info-web.lirmm.fr/collorg/86a39139-0cdb-419d-94f1-022269e7be0f END:VEVENT BEGIN:VEVENT SUMMARY:Pas de séminaire (AG)\, «TBA» DTSTART;VALUE=DATE-TIME:20151022T080000Z DTEND;VALUE=DATE-TIME:20151022T093000Z DTSTAMP;VALUE=DATE-TIME:20151006T150106Z UID:927c69a0-9836-4317-8def-b9af09b6a295 SEQUENCE:0 CREATED;VALUE=DATE-TIME:20151006T150106Z DESCRIPTION:TBA LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION: URL:https://info-web.lirmm.fr/collorg/927c69a0-9836-4317-8def-b9af09b6a295 END:VEVENT BEGIN:VEVENT SUMMARY:EunJung Kim\, «Twin-width I: tractable FO model checking» DTSTART;VALUE=DATE-TIME:20200702T090000Z DTEND;VALUE=DATE-TIME:20200702T100000Z DTSTAMP;VALUE=DATE-TIME:20200611T112317Z UID:32f73599-189c-4c86-8feb-dc810768399c SEQUENCE:2 CREATED;VALUE=DATE-TIME:20200611T112317Z DESCRIPTION:Inspired by a width invariant defined on permutations by Guill emot and Marx [SODA '14]\, we introduce the notion of twin-width on graphs and on matrices. Proper minor-closed classes\, bounded rank-width graphs\ , map graphs\, Kt-free unit d-dimensional ball graphs\, posets with antich ains of bounded size\, and proper subclasses of dimension-2 posets all hav e bounded twin-width. On all these classes (except map graphs without geom etric embedding) we show how to compute in polynomial time a sequence of d -contractions\, witness that the twin-width is at most d. We show that FO model checking\, that is deciding if a given first-order formula ϕ evalua tes to true for a given binary structure G on a domain D\, is FPT in |ϕ| on classes of bounded twin-width\, provided the witness is given. More pre cisely\, being given a d-contraction sequence for G\, our algorithm runs i n time f(d\,|ϕ|)⋅|D| where f is a computable but non-elementary functio n. We also prove that bounded twin-width is preserved by FO interpretation s and transductions (allowing operations such as squaring or complementing a graph). This unifies and significantly extends the knowledge on fixed-p arameter tractability of FO model checking on non-monotone classes\, such as the FPT algorithm on bounded-width posets by Gajarský et al. [FOCS '15 ]. \n\nJoint work with Édouard Bonnet\, Stéphan Thomassé\, and Rémi Wa trigant\n\nhttp://bbb.lirmm.fr/b/dim-ajj-ddd LAST-MODIFIED;VALUE=DATE-TIME:20201123T120827Z LOCATION:Téléseminaire URL:https://info-web.lirmm.fr/collorg/32f73599-189c-4c86-8feb-dc810768399c END:VEVENT BEGIN:VEVENT SUMMARY:Florian Hoersch\, «Reachability in arborescence packings» DTSTART;VALUE=DATE-TIME:20201105T090000Z DTEND;VALUE=DATE-TIME:20201105T110000Z DTSTAMP;VALUE=DATE-TIME:20201002T143712Z UID:0948e757-9273-4b32-b916-e83d5667e5d0 SEQUENCE:7 CREATED;VALUE=DATE-TIME:20201002T143712Z DESCRIPTION:An $r$-arborescence $B$ is an orientation of a tree in which a ll arcs are directed away from a given root $r$ and the arborescence is sa id to //span// $V(B)$. Given a digraph $D$\, an $r$-arborescence $B$ that is a subgraph of $D$ is said to be spanning if it spans $V(D)$. In 1973\, Edmonds characterized digraphs admitting a packing of $k$ spanning $r$-arb orescences for a fixed root $r$ and some integer $k$. It can readily be se en that this theorem can be generalized to allow fixed but distinct roots for the arborescences.\nIn case that some vertex cannot be reached from a given root\, the only information we obtain from Edmonds theorem is that t he desired packing does not exist. For this reason\, in 2009\, Kamiyama\, Katoh and Takizawa introduced the concept of reachability arborescences. A n $r$-arborescence is called a reachability $r$-arborescence if it spans a ll the vertices reachable from $r$ in $D$. They characterize digraphs that \, for a given root multiset $R$\, have a packing of arborescences $\\{B_r : r ∈ R\\}$ such that $B_r$ is a reachability $r$-arborescence for all $r ∈ R$. A new\, shorter proof for the theorem of Kamiyama\, Katoh and T akizawa will be presented. Being of inductive nature\, it uses a stronger form of Edmonds’ theorem and is self-contained otherwise. Further\, seve ral ways of generalizing these concepts will be mentioned. Firstly\, the c ondition on the arborescences to be spanning or reachability arborescences can be relaxed to more general conditions called matroid-based packing an d matroid-reachability-based packing. Further\, the objects of considerati on can be generalized from digraphs to mixed graphs\, dypergraphs and mixe d hypegraphs. All the proofs considered provide efficient algorithms for f inding the desired arborescences.\n\nThis is joint work with Zoltán Szige ti.\n\n\n\nTéléseminaire: [[https://bbb.lirmm.fr/b/dim-ajj-ddd]] LAST-MODIFIED;VALUE=DATE-TIME:20201104T090103Z LOCATION:Téléseminaire: https://bbb.lirmm.fr/b/dim-ajj-ddd URL:https://info-web.lirmm.fr/collorg/0948e757-9273-4b32-b916-e83d5667e5d0 END:VEVENT BEGIN:VEVENT SUMMARY:Júlio Araújo\, «Weighted proper orientations of trees and graph s of bounded treewidth» DTSTART;VALUE=DATE-TIME:20200514T090000Z DTEND;VALUE=DATE-TIME:20200514T100000Z DTSTAMP;VALUE=DATE-TIME:20200508T170741Z UID:ce353e2b-ecd7-4c0d-bd0b-de0990ef9c5a SEQUENCE:11 CREATED;VALUE=DATE-TIME:20200508T170741Z DESCRIPTION:Given a simple graph $G$\, a weight function $w:E(G)\\rightarr ow \\mathbb{N} \\setminus \\{0\\}$\, and an orientation $D$ of $G$\, we de fine $\\mu^-(D) = \\max_{v \\in V(G)} w_D^-(v)$\, where $w^-_D(v) = \\sum _{u\\in N_D^{-}(v)}w(uv)$. We say that $D$ is a \\emph{weighted proper ori entation} of $G$ if $w^-_D(u) \\neq w^-_D(v)$ whenever $u$ and $v$ are adj acent. We introduce the parameter {\\em weighted proper orientation numbe r} of $G$\, denoted by $\\overrightarrow{\\chi}(G\,w)$\, which is the mini mum\, over all weighted proper orientations $D$ of $G$\, of $\\mu^-(D)$. W hen all the weights are equal to 1\, this parameter is equal to the {\\em proper orientation number} of $G$\, which has been object of recent studi es and whose determination is NP-hard in general\, but polynomial-time sol vable on trees. We prove that the equivalent decision problem of the weigh ted proper orientation number (i.e.\, $\\overrightarrow{\\chi}(G\,w) \\leq k?$) is (weakly) NP-complete on trees but can be solved by a pseudo-polyn omial time algorithm whose running time depends on $k$. Furthermore\, we p resent a dynamic programming algorithm to determine whether a general grap h $G$ on $n$ vertices and treewidth at most $tw$ satisfies $\\overrightarr ow{\\chi}(G\,w) \\leq k$\, running in time ${\\cal O}(2^{tw^2}\\cdot k^{3t w}\\cdot tw \\cdot n)$\, and we complement this result by showing that the problem is $W[1]$-hard on general graphs parameterized by the treewidth o f $G$\, even if the weights are polynomial in $n$.\n\nhttps://moodle.umont pellier.fr/course/view.php?id=15640 LAST-MODIFIED;VALUE=DATE-TIME:20200513T090104Z LOCATION:Téléseminaire https://moodle.umontpellier.fr/course/view.php?id =15640 URL:https://info-web.lirmm.fr/collorg/ce353e2b-ecd7-4c0d-bd0b-de0990ef9c5a END:VEVENT BEGIN:VEVENT SUMMARY:Guilherme D. da Fonseca\, «On the ratio between perfect matchings and maximum weight matchings» DTSTART;VALUE=DATE-TIME:20141002T083000Z DTEND;VALUE=DATE-TIME:20141002T093000Z DTSTAMP;VALUE=DATE-TIME:20140930T120634Z UID:2d143255-c8d5-4f44-8851-9cc0d76bc249 SEQUENCE:0 CREATED;VALUE=DATE-TIME:20140930T120634Z DESCRIPTION:Given a graph G that admits a perfect matching\, the parameter eta(G) is defined as follows. Among all positive edge weight assignments\ , eta(G) is the minimum ratio between the maximum weight of (i) a perfect matching and (ii) any matching. In this talk we present new and previous r esults on the parameter eta. Among them\, a characterization of graphs wit h eta(G)=0 and eta(G) = 1 and the exact value of eta for all grids\, bipar tite cylindrical grids\, and bipartite toroidal grids.\n\nJoint work with: Diana Sasaki and Bernard Ries. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:LIRMM\, E.3.23 URL:https://info-web.lirmm.fr/collorg/2d143255-c8d5-4f44-8851-9cc0d76bc249 END:VEVENT BEGIN:VEVENT SUMMARY:Petru Valicov\, «Cuts in matchings» DTSTART;VALUE=DATE-TIME:20180215T090000Z DTEND;VALUE=DATE-TIME:20180215T100000Z DTSTAMP;VALUE=DATE-TIME:20180202T090420Z UID:479d91ad-c3b0-4bb5-9e3c-772611ad73c0 SEQUENCE:0 CREATED;VALUE=DATE-TIME:20180202T090420Z DESCRIPTION:In an attempt to solve the Four Color Problem\, Tait conjectur ed that every planar cubic 3-edge-connected graph is Hamiltonian. Once thi s statement was disproved\, several other related questions of the type "e very bipartite (planar) 3-edge connected cubic graph is Hamiltonian"\, em erged. On the other hand the conjecture of Neumann-Lara asserting that eve ry planar oriented graph can be vertex-partitioned into two acyclic sets\, can be seen as a directed version of Tait's conjecture. In this talk we e xplain how all these conjectures together with other similar questions fit in the same framework related to cuts in matchings. We show then a constr uction of 3-edge connected oriented graph satisfying the property that for every even subgraph E\, the graph obtained by contracting the edges of E is not strongly connected. This disproves a recent conjecture of Hochstät tler. At the end we will provide experimental evidence for Neumann-Lara's conjecture and discuss on tools that might be helpful to search for counte rexamples. Joint work with Kolja Knauer. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/479d91ad-c3b0-4bb5-9e3c-772611ad73c0 END:VEVENT BEGIN:VEVENT SUMMARY:Tom Kelly\, «On the density of critical graphs without large cliq ues» DTSTART;VALUE=DATE-TIME:20181011T080000Z DTEND;VALUE=DATE-TIME:20181011T090000Z DTSTAMP;VALUE=DATE-TIME:20180831T073342Z UID:274e2e1b-92f5-4509-abfe-d047d5eb8c34 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20180831T073342Z DESCRIPTION:A graph is k-critical if it has chromatic number k and every p roper subgraph is (k - 1)-colorable. The density of critical graphs has b een extensively studied. We present an improvement on the best known lowe r bound for the density of critical graphs without large cliques. We also discuss a connection to list-coloring and generalizations of Reed's Conje cture.\n\nJoint work with Luke Postle. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/274e2e1b-92f5-4509-abfe-d047d5eb8c34 END:VEVENT BEGIN:VEVENT SUMMARY:Rémi Watrigant\, «Complexity dichotomies for a generic hypergrap h problem» DTSTART;VALUE=DATE-TIME:20180208T090000Z DTEND;VALUE=DATE-TIME:20180208T100000Z DTSTAMP;VALUE=DATE-TIME:20180202T143939Z UID:b9d8f506-d693-4815-b0fe-af66e6af8ee2 SEQUENCE:0 CREATED;VALUE=DATE-TIME:20180202T143939Z DESCRIPTION:Given a (possibly infinite) fixed set of graphs \\F\, we say t hat a graph G overlays \\F on a hypergraph H if both G and H have the same set of vertices\, and if for every hyperedge S of H\, the subgraph of G i nduced by S contains a graph from \\F as a spanning subgraph. The \\F-Over lay Problem asks\, given a hypergraph H\, to find a graph G which \\F-over lays H\, and\, if such a graph exists\, to find one with the minimum numbe r of edges. We will first discuss the possible applications of this proble m\, e.g. structural biology\, network design or hypergraph drawing. We wil l then completely characterize the complexity of the \\F-Overlay Problem ( P or NP-hard) depending on the family \\F. Finally\, for the NP-hard cases \, we will also give some sufficient conditions on \\F leading to either F PT or W[1]-hard problems\, when parameterized by the number of edges of th e graph sought. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/b9d8f506-d693-4815-b0fe-af66e6af8ee2 END:VEVENT BEGIN:VEVENT SUMMARY:Christophe Crespelle\, «TBA» DTSTART;VALUE=DATE-TIME:20090107T230000Z DTEND;VALUE=DATE-TIME:20091215T230000Z DTSTAMP;VALUE=DATE-TIME:20190410T095439Z UID:69c19c74-8f61-46a4-83eb-39ae93115378 SEQUENCE:2 CREATED;VALUE=DATE-TIME:20190410T095439Z DESCRIPTION:TBA LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/69c19c74-8f61-46a4-83eb-39ae93115378 END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Gonçalves\, «On the colorability of rectangle intersectio n graphs» DTSTART;VALUE=DATE-TIME:20210311T090000Z DTEND;VALUE=DATE-TIME:20210311T100000Z DTSTAMP;VALUE=DATE-TIME:20210113T150233Z UID:f16749a9-370d-4681-abe3-590f5ebfbda2 SEQUENCE:10 CREATED;VALUE=DATE-TIME:20210113T150233Z DESCRIPTION:Chalermsook and Walczak proved that rectangle intersection gra phs with clique number $w$\, are $O(w\\cdot\\log w)$-colorable. This impro ves on the $O(w^2)$ bound dating from 1960. They also designed a determini stic polynomial-time $O(\\log \\log n)$-approximation algorithm for the sa me problem. This improves on previous known algorithms. This talk will be devoted to the description of these results. LAST-MODIFIED;VALUE=DATE-TIME:20210310T090102Z LOCATION:Téléseminaire: https://bbb.lirmm.fr/b/dim-ajj-ddd URL:https://info-web.lirmm.fr/collorg/f16749a9-370d-4681-abe3-590f5ebfbda2 END:VEVENT BEGIN:VEVENT SUMMARY:Ana Karolinna Maia\, «Characterizing networks admitting multiple arc-disjoint branching flows» DTSTART;VALUE=DATE-TIME:20200611T090000Z DTEND;VALUE=DATE-TIME:20200611T100000Z DTSTAMP;VALUE=DATE-TIME:20200521T131706Z UID:21ea1aaa-b719-4380-b6b4-99174e7c5dbe SEQUENCE:6 CREATED;VALUE=DATE-TIME:20200521T131706Z DESCRIPTION:An $s$-branching flow $f$ in a network $N = (D\,c)$ (where $c$ is the capacity function) is a flow that reaches every vertex in $V(D) \\ setminus \\{s\\}$ from $s$ while loosing exactly one unit of flow in each vertex other than $s$. In other words\, the difference between the flow en tering a vertex $v$ and a flow leaving a vertex $v$ is one whenever $v \\n eq s$.It is known that the hardness of the problem of finding $k$ arc-disj oint $s$-branching flows in network $N$ is linked to the capacity $c$ of t he arcs in $N$: the problem is solvable easy to compute if every arc has c apacity $n - \\ell$\, for fixed $\\ell$\, and hard in most other cases\, w ith very few cases open. We further investigate a conjecture by Costa et a l. from 2019 that aims to characterize networks admitting $k$ arc-disjoint $s$-branching flows\, generalizing a result by Bang-Jensen and Bessy that provides such characterization when all arcs have capacity $n-1$.\n\nJoin t work with: C. Carvalho\, J. Costa\, C. Linhares Sales\, R. Lopes\, N. Ni sse\n\nhttp://bbb.lirmm.fr/b/dim-ajj-ddd LAST-MODIFIED;VALUE=DATE-TIME:20200610T090103Z LOCATION:Téléseminaire URL:https://info-web.lirmm.fr/collorg/21ea1aaa-b719-4380-b6b4-99174e7c5dbe END:VEVENT BEGIN:VEVENT SUMMARY:Thi Viet Ha Nguyen\, «Graph problems motivated by (low and high) resolution models of large protein assemblies.» DTSTART;VALUE=DATE-TIME:20211014T080000Z DTEND;VALUE=DATE-TIME:20211014T090000Z DTSTAMP;VALUE=DATE-TIME:20210908T171202Z UID:4c2e1e31-e5e8-4cc7-931a-05ffa17b04a9 SEQUENCE:7 CREATED;VALUE=DATE-TIME:20210908T171202Z DESCRIPTION:Our works focus on graph problems motivated by structural biol ogy issues. A macromolecular assembly consists in a set of subunits\, each subunit may have a lot of configurations and any subunit is linked to the others by some relations.\nAt a low resolution\, given a set of subunits\ , or complexes of the assembly (where each complex is a subset of subunits )\, it simply specifies the interaction of subunits in an assembly. The gr aph problem is then given a hypergraph $H$ with a set of vertices $V(H)$ a nd a set of hyperedges $E(H)$ (each hyperedge is a subset of vertices)\, a nd asks to find a graph on $V(H)$ satisfying some constraints (bounded deg ree\, local structures).\nAt a high resolution\, given an assembly and a s et of configurations for each subunit\, the problem consists in finding a set of configurations for all subunits\, under some constraints. Then the graph problem is given a graph and a set of colors for each vertex\, to fi nd a coloring which satisfies some objective function (generalization of $ k$-coloring\, called //conflict coloring//).\nWe will present our studies on these two graph problems. The results are mainly about complexity\, the n some algorithms and experiments for the second problem. \n\nJoint works with Frédéric Cazals\, Frédéric Havet\, Dorian Mazauric and Rémi Watr igant. LAST-MODIFIED;VALUE=DATE-TIME:20211013T080103Z LOCATION:https://bbb.lirmm.fr/b/dim-ajj-ddd et C. BAT4-E3.23 Etage-Extensi on URL:https://info-web.lirmm.fr/collorg/4c2e1e31-e5e8-4cc7-931a-05ffa17b04a9 END:VEVENT BEGIN:VEVENT SUMMARY:Édouard Bonnet\, «Twin-width of matrices and ordered graphs» DTSTART;VALUE=DATE-TIME:20211209T090000Z DTEND;VALUE=DATE-TIME:20211209T100000Z DTSTAMP;VALUE=DATE-TIME:20211018T134725Z UID:50098345-61d8-427f-9a27-935eda46d49f SEQUENCE:2 CREATED;VALUE=DATE-TIME:20211018T134725Z DESCRIPTION:The twin-width of a graph $G$ can be defined as the least inte ger $d$ such that there is a sequence of length $|V(G)|$ of (strictly) coa rser and coarser partitions of its vertex set $V(G)$\, and every part $X$ of every partition $P$ of the sequence has at most d other parts $Y$ of $P $ with both at least one edge and at least one non-edge between $X$ and $Y $. Twin-width is closely tied to total orders on the vertices\, and can be extended to general binary structures. We will thus consider the twin-wid th of ordered binary structures\, or if you prefer\, matrices on a finite alphabet. This turns out to be key in understanding combinatorial\, algori thmic\, and model-theoretic properties of (hereditary) classes of those ob jects. We will see several characterizations of bounded twin-width for the se classes. The main consequences in the three domains read as follows. En umerative combinatorics: All the classes of 0\,1-matrices with superexpone ntial growth have growth at least n!. Algorithms: First-order model checki ng of ordered binary structures is tractable exactly when the twin-width i s bounded. Finite model theory: Monadically-dependent and dependent heredi tary classes of ordered binary structures are the same. In addition we get a fixed-parameter algorithm approximating matrix twin-width within a func tion of the optimum\, which is still missing for unordered graphs.\n\nJoin t work with Ugo Giocanti\, Patrice Ossona de Mendez\, Pierre Simon\, Stép han Thomassé\, and Szymon Toruńczyk. LAST-MODIFIED;VALUE=DATE-TIME:20211208T090103Z LOCATION:BAT4 l Séminaire LIRMM - RDC Entrée & https://bbb.lirmm.fr/b/di m-ajj-ddd URL:https://info-web.lirmm.fr/collorg/50098345-61d8-427f-9a27-935eda46d49f END:VEVENT BEGIN:VEVENT SUMMARY:Dieter Rautenbach\, «Reconfiguring dominating sets in minor-close d graph classes» DTSTART;VALUE=DATE-TIME:20200910T090000Z DTEND;VALUE=DATE-TIME:20200910T100000Z DTSTAMP;VALUE=DATE-TIME:20200831T113315Z UID:233f9162-df0b-4f4e-a695-18b1292681ca SEQUENCE:21 CREATED;VALUE=DATE-TIME:20200831T113315Z DESCRIPTION:For a graph G\, two dominating sets D and D' in G\, and a non- negative integer k\, the set D is said to k-//transform// to D' if there i s a sequence D_0\,…\,D_ℓ of dominating sets in G such that D=D_0\,D'=D _ℓ\,|D_i|≤k for every i∈{0\,1\,…\,ℓ}\, and D_i arises from D_{i- 1} by adding or removing one vertex for every i∈{1\,…\,ℓ}. We prove that there is some positive constant c and there are toroidal graphs G of arbitrarily large order n\, and two minimum dominating sets D and D' in G such that D k-transforms to D' only if k≥max{|D|\,|D'|}+c√n. Converse ly\, for every hereditary class **G** that has balanced separators of orde r n↦n^α for some α<1\, we prove that there is some positive constant C such that\, if G is a graph in **G** of order n\, and D and D' are two do minating sets in G\, then D k-transforms to D' for k=max{|D|\,|D'|}+⌊Cn^ α⌋. LAST-MODIFIED;VALUE=DATE-TIME:20200909T090102Z LOCATION:Bât 4\, salle du séminaire (LIRMM - RDC Entrée) 11:00 URL:https://info-web.lirmm.fr/collorg/233f9162-df0b-4f4e-a695-18b1292681ca END:VEVENT BEGIN:VEVENT SUMMARY:Mark Jones\, «On the consistency of orthology relationships» DTSTART;VALUE=DATE-TIME:20161103T090000Z DTEND;VALUE=DATE-TIME:20161103T100000Z DTSTAMP;VALUE=DATE-TIME:20161024T101757Z UID:708872ea-0446-4352-9d6d-5b0860be73ce SEQUENCE:1 CREATED;VALUE=DATE-TIME:20161024T101757Z DESCRIPTION:Orthology relations between genes are an important part of com paraitve genomics\, and a plethora of methods have been designed to infer these relations.\nOne particular property that must be maintained in orth ology relations is consistency with the (possibly unknown) evolutionary hi story of the corresponding species.\nEnforcing this property can be viewed as a problem of "embedding" one rooted tree within another.\n\nWe give th e first polynomial algorithm to decide whether a partial set C of ortholog y/paralogy relations is consistent\, even when the species tree is unknown . We also investigate a biologically meaningful optimization version of t hese problems\, in which we wish to minimize the number of duplication eve nts\; unfortunately\, we show that all these optimization problems are NP- hard and are unlikely to have good polynomial time approximation algorithm s. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/708872ea-0446-4352-9d6d-5b0860be73ce END:VEVENT BEGIN:VEVENT SUMMARY:Archontia Giannopoulou\, «Braces of Perfect Matching Width 2» DTSTART;VALUE=DATE-TIME:20190516T080000Z DTEND;VALUE=DATE-TIME:20190516T090000Z DTSTAMP;VALUE=DATE-TIME:20190427T081940Z UID:3d514309-e1c0-4593-8e69-8e712450344b SEQUENCE:1 CREATED;VALUE=DATE-TIME:20190427T081940Z DESCRIPTION:A graph G is called matching covered\nif it is connected and e very edge is contained in\na perfect matching. Perfect matching width is a \nwidth parameter for matching covered graphs\nbased on a branch decomposi tion that can be\nconsidered a generalisation of directed treewidth.\nWe s how that the perfect matching width of every\nbipartite matching covered g raph is within a factor\nof 2 of the perfect matching width of its braces. \nMoreover\, we give characterisations for braces\nof perfect matching wid th in terms of edge maximal\ngraphs similar to k-trees for undirected tree width\nand elimination orderings. The latter allows us to\nidentify braces of perfect matching width 2 in\npolynomial time and provides an algorithm to\nconstruct an optimal decomposition. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/3d514309-e1c0-4593-8e69-8e712450344b END:VEVENT BEGIN:VEVENT SUMMARY:Ignasi Sau\, «Reducing graph transversals via edge contractions» DTSTART;VALUE=DATE-TIME:20201001T080000Z DTEND;VALUE=DATE-TIME:20201001T090000Z DTSTAMP;VALUE=DATE-TIME:20200910T130424Z UID:ab522cd3-c5e6-4041-85ee-11144e10fa7c SEQUENCE:10 CREATED;VALUE=DATE-TIME:20200910T130424Z DESCRIPTION:For a graph parameter $\\pi$\, the **Contraction**($\\pi$) pro blem consists in\, given a graph $G$ and two positive integers $k\,d$\, de ciding whether one can contract at most $k$ edges of $G$ to obtain a graph in which $\\pi$ has dropped by at least $d$. Galby et al. [ISAAC 2019\, M FCS 2019] recently studied the case where $\\pi$ is the size of a minimum dominating set. We focus on graph parameters defined as the minimum size o f a vertex set that hits all the occurrences of graphs in a collection ** H** according to a fixed containment relation. We prove co-NP-hardness res ults under some assumptions on the graphs in **H**\, which in particular i mply that **Contraction**($\\pi$) is co-NP-hard even for fixed $k=d=1$ whe n $\\pi$ is the size of a minimum feedback vertex set or an odd cycle tran sversal. In sharp contrast\, we show that when $\\pi$ is the size of a min imum vertex cover\, the problem is in XP parameterized by $d$.\n\nJoint wo rk with Paloma T. Lima\, Vinicius F. dos Santos and Uéverton S. Souza\, a vailable at arXiv:2005.01460. LAST-MODIFIED;VALUE=DATE-TIME:20201001T070516Z LOCATION:Bât 5\, 01.124 (Invités\, RDC) IES - RDC Centre URL:https://info-web.lirmm.fr/collorg/ab522cd3-c5e6-4041-85ee-11144e10fa7c END:VEVENT BEGIN:VEVENT SUMMARY:Júlio Araújo\, «Some results on (circular) backbone colorings» DTSTART;VALUE=DATE-TIME:20201119T090000Z DTEND;VALUE=DATE-TIME:20201119T100000Z DTSTAMP;VALUE=DATE-TIME:20200910T151506Z UID:6de80e47-b9bb-44dd-9e57-e71d744a470e SEQUENCE:6 CREATED;VALUE=DATE-TIME:20200910T151506Z DESCRIPTION:A proper $k$-coloring of a simple graph $G$ is a function $c: V(G)\\to \\{1\,...\,k\\}$ such that\, for each edge $uv\\in E(G)$\, we hav e $1≤|c(u)-c(v)|$. Given a graph $G$ and a spanning subgraph $H$ of $G$\ , a $q$-backbone $k$-coloring of the pair $(G\,H)$ is a proper $k$-colorin g $c$ of $G$ such that $q≤|c(u)-c(v)|$ for each edge $uv$ in $E(H)$. A $ q$-backbone $k$-coloring of $(G\,H)$ is circular if $|c(u)-c(v)|≤k-q$. I n their seminal paper Broersma et al. (2007) conjectured that if $G$ is pl anar and $T$ is a spanning tree of $G$\, then $(G\,T)$ admits a 2-backbone 6-coloring. They also conjectured that if $G$ is planar and $M$ is a span ning subgraph of maximum degree one\, then $(G\,M)$ admits a 2-backbone 5- coloring. Similar conjectures for the circular case have been proposed (wi th one extra color). \n\nIn this talk\, we present some results related t o these conjectures and their corresponding circular versions obtained in distinct works coauthored by Frédéric Havet\, Matthieu Schmitt\, Ana Sil va\, Fabricio Benevides\, Alexandre Cezar and Camila Araujo.\n\n\n\nTélé seminaire: [[https://bbb.lirmm.fr/b/dim-ajj-ddd]] LAST-MODIFIED;VALUE=DATE-TIME:20201118T090102Z LOCATION:Téléseminaire: https://bbb.lirmm.fr/b/dim-ajj-ddd URL:https://info-web.lirmm.fr/collorg/6de80e47-b9bb-44dd-9e57-e71d744a470e END:VEVENT BEGIN:VEVENT SUMMARY:Benjamin Merlin Bumpus\, «Structured Decompositions: recursive da ta and recursive algorithms» DTSTART;VALUE=DATE-TIME:20220915T080000Z DTEND;VALUE=DATE-TIME:20220915T090000Z DTSTAMP;VALUE=DATE-TIME:20220613T081541Z UID:1bdc7ad4-a85b-4fbc-b526-76ea0fa2e483 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20220613T081541Z DESCRIPTION:What is recursive structure? And how can we exploit it algorit hmically? In this talk I will give as general an answer to these questions as I can by calling upon the new notion of structured decompositions. Thi s is a category-theoretic formalism that Jade Master\, Zoltan Kocsis and I recently introduced which yields a vast generalisation of tree-width to a rbitrary categories. I will explain — assuming no prior knowledge at all of category theory — how to make use of structured decompositions for t hree purposes: (1) defining new tree-width-like invariants\, (2) relating these decompositions to each-other via functors and (3) how one might go a bout proving algorithmic meta-theorems using the language of category theo ry. This is ongoing\, multidisciplinary work. As such it requires lots peo ple with different types of expertise\, so you should consider this talk i s an invitation to get involved! LAST-MODIFIED;VALUE=DATE-TIME:20220914T080103Z LOCATION:https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/1bdc7ad4-a85b-4fbc-b526-76ea0fa2e483 END:VEVENT BEGIN:VEVENT SUMMARY:Stéphane Bessy\, «Exponential Independence in Subcubic Graphs» DTSTART;VALUE=DATE-TIME:20210401T080000Z DTEND;VALUE=DATE-TIME:20210401T090000Z DTSTAMP;VALUE=DATE-TIME:20210324T072539Z UID:237d4d9a-6ac1-4e1b-94f7-9319c6b38ed0 SEQUENCE:6 CREATED;VALUE=DATE-TIME:20210324T072539Z DESCRIPTION:A set $S$ of vertices of a graph $G$ is exponentially independ ent if\, for every vertex $u$ in $S$\, $\\sum_{v∈S\\setminus \\{u\\}}(1/ 2)^{{\\rm dist}(G\,S) (u\,v)−1} < 1$\, where ${\\rm dist}(G\,S)(u\, v)$ is the distance between $u$ and $v$ in the graph $G − (S \\setminus \\{ u\, v\\})$. The exponential independence number $αe(G)$ of $G$ is the ma ximum order of an exponentially independent set in $G$. In this work we pr esent several bounds on this parameter and highlight some of the many rela ted open problems. In particular\, we prove that subcubic graphs of order n have exponentially independent sets of order $Ω(n/\\log^2 (n))$\, that the infinite cubic tree has no exponentially independent set of positive d ensity\, and that subcubic trees of order n have exponentially independent sets of order $(n + 3)/4$.\n\nJoint work with D. Rautenbach and J. Pardey \, Ulm University LAST-MODIFIED;VALUE=DATE-TIME:20210331T080102Z LOCATION:Téleseminaire: https://bbb.lirmm.fr/b/dim-ajj-ddd URL:https://info-web.lirmm.fr/collorg/237d4d9a-6ac1-4e1b-94f7-9319c6b38ed0 END:VEVENT BEGIN:VEVENT SUMMARY:Jean-Florent Raymond\, «Packings induits de cycles» DTSTART;VALUE=DATE-TIME:20140925T080000Z DTEND;VALUE=DATE-TIME:20140925T090000Z DTSTAMP;VALUE=DATE-TIME:20150201T014401Z UID:4954ac63-1157-43b2-9d25-6376cc2c067f SEQUENCE:1 CREATED;VALUE=DATE-TIME:20150201T014401Z DESCRIPTION:Deux cycles d'un graphes sont mutuellement induits s'il n'y a pas d'arêtes entre eux dans le graphe. Etant donné un graphe G et un ent ier r\, peut-on facilement savoir si G contient r cycles 2 à 2 induits ? Ce problème\, que nous appellerons Cycles-Induits\, n'a pas de noyau poly nomial quand il est paramétrisé par r sous des hypothèses courantes de complexité\, d'après les résultats de Bodlaender\, Thomassé et Yeo (20 12)\, qui ont étudié sa version non-induite.\n\nEn utilisant des argumen ts simples\, nous montrons que Cycles-Induits a un noyau de taille O(Δ²) pour r = 2 et O(rΔ² log(rΔ)) pour r > 2. Une conséquence est que la v ersion non-induite du problème a aussi un noyau polynomial pour cette par amétrisation.\n\nRésultats obtenus en collaboration avec Aistis Atminas (Université de Warwick) et Marcin Kamiński (Université de Varsovie). LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/4954ac63-1157-43b2-9d25-6376cc2c067f END:VEVENT BEGIN:VEVENT SUMMARY:Marin Bougeret\, «Kernelization of Vertex Cover under structural parameterizations» DTSTART;VALUE=DATE-TIME:20200924T080000Z DTEND;VALUE=DATE-TIME:20200924T090000Z DTSTAMP;VALUE=DATE-TIME:20200910T141422Z UID:68e3d9a9-6c5e-4bd7-9f42-67c41c44b37c SEQUENCE:10 CREATED;VALUE=DATE-TIME:20200910T141422Z DESCRIPTION:We consider here the area of Parameterized Complexity called «structural parameterization». The idea is to analyze the computational complexity of a problem taking into account a structural property of the i nput graph\, which captures\, informally speaking\, its inherent "complexi ty" according to some measure. There is a whole ecology of structural para meters\, cf. for instance [1]. For example\, for **VC** (the classical Ver tex Cover problem consisting in\, given a graph $G$ and an integer paramet er $k$\, deciding whether $G$ contains at most $k$ vertices intersecting a ll its edges) one can consider **VC** parameterized by $κ$\, where the pa rameter $κ(G\, k)$ is not necessarily $k$\, but a function depending on $ G$\, such as the treewidth of $G$. Kernelization considering structural pa rameters has grown dramatically thanks to [2]\, which proves that **VC**/ **FVS** (meaning **VC** parameterized by the size of a feedback vertex set ) admits a polynomial kernel\, that is\, a polynomial-time algorithm that transforms an instance into an equivalent one with size polynomially bound ed in terms of the parameter. As occurs quite often in Parameterized Compl exity\, the Vertex Cover problem played a triggering role in this area as a "simple" but still fundamental problem\, for which the ultimate quest wo uld be characterize for which graph parameters $p$ the problem **VC**$/p$ admits a polynomial kernel\, subject to reasonable complexity assumptions. This quest has motivated a number of recent research articles. In this ta lk\, I will present some techniques that are used in several papers of thi s area. The goal is to\n\n\n1) understand the link between Minimal Blockin g Sets and Structural Kernelization of **VC**.\n2) explain how kernels lik e [2\,4\,5] are obtained\n3) explain what is the result of [4] which almos t answer the ultimate quest\n\nThis talk is based on joint work with Bart M. P. Jansen and Ignasi Sau\n\n\n\nReferences:\n\n[1] Michael Fellows\, Ba rt M. P. Jansen\, and Frances Rosamond: Towards fully multivariate algorit hmics: Parameter ecology and the deconstruction of computational complexit y. European Journal of Combinatorics\, 2013.\n\n[2] Bart M. P. Jansen and Hans L. Bodlaender: Vertex Cover Kernelization Revisited - Upper and Lowe r Bounds for a Refined Parameter. Theory of Computing Systems\, 2013.\n\n[ 3] Eva-Maria C. Hols\, Stefan Kratsch\, and Astrid Pieterse. Elimination d istances\, blocking sets\,and kernels for vertex cover.\n\n[4] Marin Bouge ret\, Bart M. P. Jansen\, and Ignasi Sau: Bridge-depth characterizes which structural parameterizations of Vertex Cover admit a polynomial kernel. I CALP 2020\n\n[5] Marin Bougeret and Ignasi Sau. How much does a tre edepth modulator help to obtain polynomial kernels beyond sparse graph s? Algorithmica\, 2018 LAST-MODIFIED;VALUE=DATE-TIME:20210324T120610Z LOCATION:Bât 5\, 01.124 (Invités\, RDC) IES - RDC Centre URL:https://info-web.lirmm.fr/collorg/68e3d9a9-6c5e-4bd7-9f42-67c41c44b37c END:VEVENT BEGIN:VEVENT SUMMARY:Jayakrishnan Madathil\, «Connecting the Dots (with Minimum Crossi ngs)» DTSTART;VALUE=DATE-TIME:20190328T090000Z DTEND;VALUE=DATE-TIME:20190328T100000Z DTSTAMP;VALUE=DATE-TIME:20190325T102339Z UID:ccf926fa-85b4-47a4-b779-7cbcd065e3ca SEQUENCE:0 CREATED;VALUE=DATE-TIME:20190325T102339Z DESCRIPTION:We study a prototype "crossing minimization" problem. Consider a graph G embedded in the Euclidean plane as follows: the vertices are in distinct points in the plane\, and the edges are embedded as line segment s between their endpoints. A crossing in G is a pair of edges that interse ct (at a point other than their possibly common endpoints). \nWe are inter ested in testing whether G has a subgraph with certain properties (such as \, being a perfect matching)\, and at the same time\, has only a given num ber of crossings.\n\nAs a starting point\, we consider the special case wh en G is a two-layered graph\, i.e.\, a bipartite graph with the following embedding. Let V(G)=X union Y be the vertex bipartition\; the vertices of X are embedded on a line L_1\, and the vertices of Y on a different line L _2 that is parallel to L_1. In this case\, the crossings in G are uniquely determined by the relative ordering of vertices of X and Y on the lines L _1 and L_2\, respectively. \nSpecifically\, we study the following problem s. Here\, the input is a two-layered graph G and a non-negative integer k. \n\n1. Crossing Minimizing Perfect Matching: The problem is to test wheth er G has a perfect matching with at most k crossings. We show that this pr oblem is NP-hard\, but admits a 2^{O(sqrt(k))} poly(n) algorithm and a ker nel with O(k^2) vertices.\n\n2. Crossing Minimizing Hamiltonian Path: The problem is to test whether G has a Hamiltonian path with at most k crossin gs. We show that this problem is NP-hard\, but admits a 2^{O(sqrt(k) log k )} poly(n) algorithm and a kernel with O(k^2) vertices.\n\n3. Crossing Min imizing (s\,t)-path: The problem is to test whether G has a path (between two given vertices s and t) with at most k crossings. We show that this pr oblem is W[1]-hard\, but admits an n^{O(k)} algorithm.\n\nThe talk will fo cus mainly on the Crossing Minimizing Perfect Matching problem. This is jo int work with Akanksha Agrawal\, Grzegorz Guśpiel\, Saket Saurabh and Mei rav Zehavi. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/ccf926fa-85b4-47a4-b779-7cbcd065e3ca END:VEVENT BEGIN:VEVENT SUMMARY:Christophe Paul\, «Connected search against a lazy robber» DTSTART;VALUE=DATE-TIME:20170608T080000Z DTEND;VALUE=DATE-TIME:20170608T090000Z DTSTAMP;VALUE=DATE-TIME:20170518T115755Z UID:47331550-46fa-450c-82c4-87148736d0e5 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20170518T115755Z DESCRIPTION:Abstract: The node search game against a lazy/agile (invisible ) robber has been introduced as a search-game analogue of the graph parame ters of treewidth/pathwidth. In the “connected” variants of the above two games\, we additionally demand that\, at each moment of the search\, t he “clean” territories are connected. The connected search game agains t an agile and invisible robber has been extensively examined. The monoton e variant (where we also demand that the clean territories are progressive ly increasing) of this game\, corresponds to the graph parameter of connec ted pathwidth and has been shown that its value cannot be more than the do uble (asymptotically) of its non-connected counterpart. This implied that the “price of connectivity” is bounded by 2 for the case of an agile r obber. In this paper we initiate the study of the connected variant of thi s search game where the robber is lazy\, in the sense that he/she moves on ly when the searchers strategy threatens the location that he/she currentl y occupies. We introduce two alternative graph-theoretical formulations of its monotone variant\, one in terms of (connected) layouts and one on ter ms of (connected) tree decompositions\, leading to the graph parameter of connected treewidth. For this “lazy-robber” variant we prove that ther e is no bound in the price of connectivity\, which comes in contrast to th e case of an agile robber. We also observe that the corresponding paramete r\, i.e. connected treewidth\, is closed under contractions and we study t he contraction-obstruction set class of the class of graphs with connected treewidth at most k. It follows that this set is infinite for every k ≥ 2. We also provide a complete characterisation for the case where k = 2. This is joint work with Isolde Adler and Dimitrios M. Thilikos. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/47331550-46fa-450c-82c4-87148736d0e5 END:VEVENT BEGIN:VEVENT SUMMARY:Matthieu Rosenfeld\, «A new Approach to Non-Repetitive Colorings of Graphs of Bounded Degree» DTSTART;VALUE=DATE-TIME:20201008T080000Z DTEND;VALUE=DATE-TIME:20201008T090000Z DTSTAMP;VALUE=DATE-TIME:20200910T130251Z UID:99a77eb6-59f6-4e4c-b061-b2e553ebdd43 SEQUENCE:4 CREATED;VALUE=DATE-TIME:20200910T130251Z DESCRIPTION:We propose a new proof technique that applies to the same prob lems as the Lovasz Local Lemma or the entropy-compression method. In term s of upper-bounds our approach seems to be as strong as entropy-compressio n\, but the proofs are more elementary and shorter. A path $(v_1\,\,\,...\ , v_{2n})$ is repetitively colored by a coloring $C$ if for all $t$\, $C(v _t)= C(v_{t+n})$. A coloring is non-repetitive if none of the paths is rep etitively colored. I will present the proof technique in the context of no n-repetitive colorings and use it to improve upper-bounds relating differe nt non-repetitive chromatic numbers to the maximal degree of a graph. LAST-MODIFIED;VALUE=DATE-TIME:20201123T120844Z LOCATION:BAT 4\, Salle de séminaire LIRMM - RDC Entrée URL:https://info-web.lirmm.fr/collorg/99a77eb6-59f6-4e4c-b061-b2e553ebdd43 END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Gonçalves\, «Planar graphs as L-intersection or L-contact graphs : part 2» DTSTART;VALUE=DATE-TIME:20171116T090000Z DTEND;VALUE=DATE-TIME:20171116T100000Z DTSTAMP;VALUE=DATE-TIME:20171025T134234Z UID:d66753f9-b6b8-4a02-9239-295ab8402514 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20171025T134234Z DESCRIPTION:Cet exposé est la suite de l'exposé ci-dessous.\n\nIl sera p ossible de suivre celui-là sans avoir suivi le précédent.\n\n********** *****************************\nEn collaboration avec Lucas Isenmann et Cla ire Pennarun\n\nThe L-intersection graphs are the graphs that have a repre sentation as intersection graphs of axis parallel shapes in the plane. A s ubfamily of these graphs are {L\, |\, -}-contact graphs which are the cont act graphs of axis parallel L\, |\, and - shapes in the plane. We prove he re two results that were conjectured by Chaplick and Ueckerdt in 2013. We show that planar graphs are L-intersection graphs\, and that triangle-free planar graphs are {L\, |\, -}-contact graphs. These results are obtained by a new and simple decomposition technique for 4-connected triangulations . Our results also provide a much simpler proof of the known fact that pla nar graphs are segment intersection graphs. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/d66753f9-b6b8-4a02-9239-295ab8402514 END:VEVENT BEGIN:VEVENT SUMMARY:Ivan Rasskin\, «Construction d'entrelacs avec des empilements de boules à l'aide de la géométrie Lorentzienne discrète» DTSTART;VALUE=DATE-TIME:20201210T090000Z DTEND;VALUE=DATE-TIME:20201210T100000Z DTSTAMP;VALUE=DATE-TIME:20201120T095131Z UID:0c49d40b-ca46-49d6-9665-3454469ea19b SEQUENCE:2 CREATED;VALUE=DATE-TIME:20201120T095131Z DESCRIPTION:Grâce au célèbre théorème de Koebe-Andreev-Thurston on sa it que tout graphe planaire peut être représenté comme le graphe de con tact d'un empilement de disques dans le plan. Cependant\, aucune caractér isation complète a été donnée pour les graphes de contact des empileme nts de boules dans l'espace. Une de famille de graphes qui se pourrait se porter comme candidat naturel est la famille des graphes qui ne sont pas i ntrinsèquement noués ou intrinsèquement entrelacés\, i. e.\, les graph es que l'on peut plonger dans l'espace sans que aucun de ses cycles formen t un entrelacs non-trivial. Réciproquement\, on pourrait se demander si p our un entrelacs L donné quel est le nombre minimal de boules dans un emp ilement dont le graphe de contact contient une collection de cycles forman t L. Ce nombre\, appelé le ball number de L\, est un invariant de noeuds introduit par Maheara qui a été peu exploré. Dans cette exposé je mett rai en évidence comment on peut utiliser la géométrie Lorentzienne disc rète pour montrer d'une part que la famille des graphes intrinsèquement entrelacés et la famille des graphes de contact des empilement de boules ne sont pas comparables et d'autre part que le ball number d'un entrelacs à n croisements est au plus de 5n. \n\nCeci est un travail en collaborati on avec J. Ramírez.\n\nTéléseminaire: [[https://bbb.lirmm.fr/b/dim-ajj- ddd]] LAST-MODIFIED;VALUE=DATE-TIME:20201209T090103Z LOCATION:Téléseminaire https://bbb.lirmm.fr/b/dim-ajj-ddd URL:https://info-web.lirmm.fr/collorg/0c49d40b-ca46-49d6-9665-3454469ea19b END:VEVENT BEGIN:VEVENT SUMMARY:Dieter Rautenbach \, «Zero forcing» DTSTART;VALUE=DATE-TIME:20160922T080000Z DTEND;VALUE=DATE-TIME:20160922T090000Z DTSTAMP;VALUE=DATE-TIME:20160825T145231Z UID:2fa3e1d0-ad47-4943-9105-aa56dd67e686 SEQUENCE:3 CREATED;VALUE=DATE-TIME:20160825T145231Z DESCRIPTION:A set $Z$ of vertices of a graph $G$ is a zero forcing set of $G$ if \ninitially labeling all vertices in $Z$ with $1$ and all remaining vertices of $G$ with $0$\, and then\, iteratively and as long as possible \, changing the label of some vertex $u$ from $0$ to $1$ if $u$ is the on ly neighbor with label $0$ of some vertex with label $1$\, results in the entire vertex set of $G$.\n\nThe zero forcing number $Z(G)$\, defined as t he minimum order of a zero forcing set of $G$\, was proposed as an upper b ound of the corank of matrices associated with $G$\, and was also consider ed in connection with quantum physics and logic circuits. \n\nIn view of t he computational hardness of the zero forcing number\, upper and lower bou nds are of interest. We discuss such bounds and some of the corresponding extremal graphs.\n\nJoint work with M. Gentner\, L.D. Penso\, and U.S. Sou za. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/2fa3e1d0-ad47-4943-9105-aa56dd67e686 END:VEVENT BEGIN:VEVENT SUMMARY:Marthe Bonamy\, «Distributed coloring in sparse graphs with fewer colors» DTSTART;VALUE=DATE-TIME:20180412T083000Z DTEND;VALUE=DATE-TIME:20180412T093000Z DTSTAMP;VALUE=DATE-TIME:20180404T082914Z UID:aa632d25-304a-4237-adbe-532078c4d053 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20180404T082914Z DESCRIPTION:We are concerned with efficiently coloring sparse graphs in\nt he distributed setting with as few colors as possible. According to\nthe c elebrated Four Color Theorem\, planar graphs can be colored with\nat most 4 colors\, and the proof gives a (sequential) quadratic\nalgorithm finding such a coloring. A natural problem is to improve\nthis complexity in the distributed setting. Using the fact that planar\ngraphs contain linearly m any vertices of degree at most 6\, Goldberg\,\nPlotkin\, and Shannon obtai ned a deterministic distributed algorithm\ncoloring n-vertex planar graphs with 7 colors in O(logn) rounds. Here\,\nwe show how to color planar grap hs with 6 colors in polylog(n) rounds.\nOur algorithm indeed works more ge nerally in the list-coloring setting\nand for sparse graphs (for such grap hs we improve by at least one the\nnumber of colors resulting from an effi cient algorithm of Barenboim\nand Elkin\, at the expense of a slightly wor st complexity). Our bounds\non the number of colors turn out to be quite s harp in general. Among\nother results\, we show that no distributed algori thm can color every\nn-vertex planar graph with 4 colors in o(n) rounds. T his is joint work\nwith Pierre Aboulker\, Nicolas Bousquet and Louis Esper et. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/aa632d25-304a-4237-adbe-532078c4d053 END:VEVENT BEGIN:VEVENT SUMMARY:Pas de séminaire (vacances)\, «TBA» DTSTART;VALUE=DATE-TIME:20151029T090000Z DTEND;VALUE=DATE-TIME:20151029T103000Z DTSTAMP;VALUE=DATE-TIME:20150923T082006Z UID:125b153a-df11-4b45-85bf-6b291db8808a SEQUENCE:5 CREATED;VALUE=DATE-TIME:20150923T082006Z DESCRIPTION:TBA LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/125b153a-df11-4b45-85bf-6b291db8808a END:VEVENT BEGIN:VEVENT SUMMARY:Aniket Basu Roy\, «Effectiveness of Local Search for Geometric Pa cking and Covering Problems» DTSTART;VALUE=DATE-TIME:20181018T083000Z DTEND;VALUE=DATE-TIME:20181018T093000Z DTSTAMP;VALUE=DATE-TIME:20180829T130251Z UID:25e21fd8-4ef9-4451-a4cf-7c93d9279bfb SEQUENCE:5 CREATED;VALUE=DATE-TIME:20180829T130251Z DESCRIPTION:In the words of Papadimitriou and Steiglitz\, “local search is based on what is perhaps the oldest optimization method — trial and e rror.” In this talk\, we are going to discuss a local search framework f or geometric optimization problems that yields a polynomial time approxima tion scheme (PTAS) which was introduced independently by two different pap ers in 2009. Then we are going to see its effectiveness in packing non-pie rcing regions and guarding orthogonal art galleries with mobile guards. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/25e21fd8-4ef9-4451-a4cf-7c93d9279bfb END:VEVENT BEGIN:VEVENT SUMMARY:Rémi de Joannis de Verclos\, «Easily testable properties of dens e graphs» DTSTART;VALUE=DATE-TIME:20160915T080000Z DTEND;VALUE=DATE-TIME:20160915T090000Z DTSTAMP;VALUE=DATE-TIME:20160909T130003Z UID:32b59004-affd-446f-9432-a8effa34d884 SEQUENCE:3 CREATED;VALUE=DATE-TIME:20160909T130003Z DESCRIPTION:A graph of size $n$ is $\\epsilon$-far from having a property P if one\nhave to add or delete at least $\\epsilon n^2$ edges of G to hav e a graph\nsatisfying P. A graph property P is testable if for every $\\ep silon$ there is a\nconstant $m(\\epsilon)$ such that it is possible to dis tinguish (with one-sided\nerror) between graphs of P and graphs that are $ \\epsilon$-far of P with an algorithm that examines only a random induced subgraph of size $m(\\epsilon)$ (which does not depend on the size\nof the graph). It has been proven that every hereditary property is\ntestable bu t the query complexity $m(\\epsilon)$ needed for this prove is an\nexponen tial tower in $\\frac{1}{\\epsilon}$.\nFollowing a work of Alon and Fox\, we seek to classify graph classes for\nwhich this query complexity $m(\\ep silon)$ is a polynomial in $\\frac{1}{\\epsilon}$\, which are called ”ea sily testable". We prove that the class of interval graphs and some subcla sses of intervals graphs are easily testable. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/32b59004-affd-446f-9432-a8effa34d884 END:VEVENT BEGIN:VEVENT SUMMARY:Jorgen Bang-Jensen\, «Completing partial orientations to digraphs with special properties» DTSTART;VALUE=DATE-TIME:20170601T080000Z DTEND;VALUE=DATE-TIME:20170601T090000Z DTSTAMP;VALUE=DATE-TIME:20170529T143302Z UID:e8eb6164-3eb6-4bf9-ad62-1b415eda3013 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20170529T143302Z DESCRIPTION:A mixed graph is a graph which may contain both (unoriented) e dges\nand arcs. We denote such a graph by M = (V\, E ∪ A)\, where E is t he set of\nunoriented edges and A\, the set of arcs\, that are already ori ented. Let C be a class of digraphs\, e.g. C could be the class of acyclic digraphs\, tournaments\, strong digraphs\, digraphs with k-disjoint out-b ranchings etc. The Orientation completion problem for the class C is the f ollowing: given a mixed graph M = (V\, E ∪ A)\; decide whether it is pos sible to orient the edges of E the a set of arcs A in such a way that the resulting digraph D = (V\, A ∪ A) belongs to the class C?\nMany problems fit into this framework\, such as:\n• Given a mixed graph M = (V\, E ∪ A) which is strongly connected (when\nwe allow each edge in E to be tr aversed in any direction). Can we complete\nthe orientation such that we o btain a strong digraph.\n• Same problem as above but now we want to pres erve high edge-connectivity.\n• Again the same but now we want to preser ve high vertex connectivity\n• Given an acyclic mixed graph M = (V\, E ∪A) (meaning that A induces an\nacyclic digraph) and a vertex s\; can we complete the orientation so that\nwe obtain an acyclic digraph with an ou t-branching from s?\n• Given an acyclic mixed graph M = (V\, E ∪ A) an d two vertices s\, t\; can\nwe complete the orientation so that we obtain an acyclic digraph with an\n(s\, t)-path?\nI will discuss these and severa l other problems in my talk. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/e8eb6164-3eb6-4bf9-ad62-1b415eda3013 END:VEVENT BEGIN:VEVENT SUMMARY:Arnaud Sallaberry\, «Hypergraphes planaires : résultats et probl ème ouvert» DTSTART;VALUE=DATE-TIME:20170202T090000Z DTEND;VALUE=DATE-TIME:20170202T100000Z DTSTAMP;VALUE=DATE-TIME:20161214T091539Z UID:b40dcc2c-5826-4ab3-a40c-916388a20eb5 SEQUENCE:0 CREATED;VALUE=DATE-TIME:20161214T091539Z DESCRIPTION:Un hypergraphe est une paire H=(V\,A) où V est un ensemble de sommets et A est un ensemble de sous-ensembles non vides de V. Une approc he classique pour représenter graphiquement un hypergraphe consiste à de ssiner les sommets sous forme de points et les hyperarêtes sous forme de polygones. Le principal enjeu consiste alors à trouver un positionnement des sommets tel que les intersections des polygones dans le plan ne contie nne que les sommets des hyperarêtes correspondant à ces polygones. La no tion d'hypergraphe planaire a été introduite pour caractériser les hype rgraphes pouvant être dessinés de cette façon. Plusieurs définitions f ormelles ont été proposées. La plus générale est basée sur la notion de support. Un graphe support d'un hypergraphe H=(V\,A) est un graphe G=( V\,E) dans lequel les sous-graphes induits par les sommets de chaque hyper arête sont connexes. Un hypergraphe est dit planaire si et seulement si i l possède un graphe support planaire. Dans cet exposé\, je présenterai plusieurs problèmes résolus et un ouvert liés à la planarité des hype rgraphes. Plusieurs de ces résultats reposent sur une nouvelle définitio n des composantes bi-connexes d'un hypergraphe. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/b40dcc2c-5826-4ab3-a40c-916388a20eb5 END:VEVENT BEGIN:VEVENT SUMMARY:François Dross\, «Partition of sparse graphs into independent se ts\, forests and forests of bounded degree» DTSTART;VALUE=DATE-TIME:20170105T090000Z DTEND;VALUE=DATE-TIME:20170105T100000Z DTSTAMP;VALUE=DATE-TIME:20170102T133000Z UID:a0854149-6d5e-42e9-ae23-1e3900dafc58 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20170102T133000Z DESCRIPTION:As a generalization of proper colouring\, we study vertex part itions of graphs into some graphs with particular properties\, in particul ar independent sets\, forests and forests with bounded degree. Proper colo urings correspond to partitions into independent sets.\n\n We will see som e sufficient conditions for sparse graphs to admit such partitions. In par ticular\, every planar graph of girth at least 4 admits a partition into a forest and a forest of maximum degree at most 5\, and every planar graph of girth at least 7\, 8 and 10 admits a partition into an independent set and a forest of maximum degree at most 5\, 3 and 2 respectively. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/a0854149-6d5e-42e9-ae23-1e3900dafc58 END:VEVENT BEGIN:VEVENT SUMMARY:Pascal Ochem\, «H-coloring dans les graphes planaires.» DTSTART;VALUE=DATE-TIME:20171123T090000Z DTEND;VALUE=DATE-TIME:20171123T100000Z DTSTAMP;VALUE=DATE-TIME:20171026T075324Z UID:6233ce8f-defa-4cd9-b34d-7e028e6265d1 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20171026T075324Z DESCRIPTION:Pour un graphe H fixé\, le problème H-coloring\ndemande si l e graphe d'entrée G admet un homomorphisme vers H\,\nc'est-à-dire si un mapping m: V(G) -> v(H) tel que\nsi uv est une arête de G\, alors m(h)m(v ) est une arête de H.\nHell et Nesetril ont montré que H-coloring est po lynomial\nsi H est biparti et NP-complet sinon.\nD'abord\, je donnerai le début de cette preuve.\nEnsuite\, on s'intéressera au cas où G est plan aire : planar H-coloring.\nOn verra que planar H-coloring est polynomial s i H est la clique à au moins 4 sommets ou le graphe de Clebsh. Aussi plan ar H-coloring est NP-complet si H est un cycle impair\, le carré d'un cyc le pair\, ou l'icosaèdre. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/6233ce8f-defa-4cd9-b34d-7e028e6265d1 END:VEVENT BEGIN:VEVENT SUMMARY:Marthe Bonamy\, «Tight lower bounds for the complexity of multico loring» DTSTART;VALUE=DATE-TIME:20161215T090000Z DTEND;VALUE=DATE-TIME:20161215T100000Z DTSTAMP;VALUE=DATE-TIME:20160930T072609Z UID:37804dd9-7323-4021-94cb-d58b25524e94 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20160930T072609Z DESCRIPTION:In the multicoloring problem\, also known as (a:b) or b-fold c oloring\, we are given a graph G and a set of a colors\, and the task is t o assign a subset of b colors to each vertex of G so that adjacent vertice s receive disjoint color subsets. This natural generalization of the class ic coloring problem (the b=1 case) is equivalent to finding a homomorphism to the Kneser graph with parameters a and b. It is tightly connected with the fractional chromatic number\, and has multiple applications within co mputer science.\n\nWe study the complexity of determining whether a graph has an (a:b)-coloring. Nederlof showed in 2008 a $(b+1)^n n^{O(1)}$-time a lgorithm for (a:b)-coloring. Our main result is that this is essentially o ptimal: there is no algorithm with running time $2^{o(log b)⋅n}$ unless the ETH fails. The crucial ingredient in our hardness reduction is the usa ge of detecting matrices of Lindström (1965)\, which is a combinatorial t ool that\, to the best of our knowledge\, has not yet been used for provin g complexity lower bounds. As a side result\, we also prove that the exist ing algorithms for the r-monomial detection problem are optimal under ETH. \n\nThis is joint work with Łukasz Kowalik\, Michał Pilipczuk\, Arkadi usz Socała and Marcin Wrochna (University of Warsaw). LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/37804dd9-7323-4021-94cb-d58b25524e94 END:VEVENT BEGIN:VEVENT SUMMARY:Marc Noy\, «Logical limit laws in combinatorics» DTSTART;VALUE=DATE-TIME:20141016T073000Z DTEND;VALUE=DATE-TIME:20141016T090000Z DTSTAMP;VALUE=DATE-TIME:20140930T131829Z UID:37fe2045-6265-4ea0-92e8-f629ff1dac9c SEQUENCE:0 CREATED;VALUE=DATE-TIME:20140930T131829Z DESCRIPTION:Let A be a class of combinatorial structures equipped\, for ea ch N\, with a probability distribution on the collection of objects of siz e N. Given a sentence S in some logical language\, we are interested in th e limiting probability P(S) that S is satisfied among all objects of size N\, as N goes to infinity. If P(S) is either 0 or 1 for each sentence S\, we say that the zero-one law holds. The first result of this kind was obta ined by Glebskii et al. in 1969 for the class of labelled graphs and sente nces in first order logic (FO). Compton (1987) obtained in some cases zero -one laws solely from properties of the counting function of the class A. Later he extended it to monadic second order logic (MSO)\, which is FO log ic plus quantification over unary relations. More recently McCoy (2002) pr oved a zero-one law in MSO logic for labelled trees. We provide a signific ant extension of McCoy’s result to classes of graphs closed under taking minors. As an example\, we prove the MSO zero-one law for connected plana r graphs and a convergence law (every sentence has a limit\, not necessari ly 0 or 1) for all planar graphs. We also determine the closure of the set of all possible limiting probabilities\, both in FO and MSO. For the proo fs we use classical tools from combinatorial logic\, in particular Ehrenfe ucht-Fraïssé games\, and properties of random graphs from a minor-closed class. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:LIRMM\, E.3.23 URL:https://info-web.lirmm.fr/collorg/37fe2045-6265-4ea0-92e8-f629ff1dac9c END:VEVENT BEGIN:VEVENT SUMMARY:Emeric Gioan\, «On six expressions of the Tutte polynomial of a g raph (on a linearly ordered set of edges)» DTSTART;VALUE=DATE-TIME:20170119T090000Z DTEND;VALUE=DATE-TIME:20170119T100000Z DTSTAMP;VALUE=DATE-TIME:20170105T124048Z UID:f75a99d5-2aca-4d95-befd-aa7f2efc21d6 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20170105T124048Z DESCRIPTION:I will present six interrelated general expressions of the Tut te polynomial of a graph\, that are available as soon as the set of edges is linearly ordered\, and that witness combinatorial properties of such a graph:\n\n- the classical enumeration of spanning tree activities\;\n\n- i ts refinement into a four variable expression in terms of subset activitie s (that corresponds to the classical partition of the set of edge subsets into boolean intervals)\;\n\n- the enumeration of orientation-activities f or directed graphs\;\n\n- its refinement into a four variable expression i n terms of subset orientation-activities (that corresponds to the partitio n of the set of orientations into active partition reversal classes)\;\n\n - the convolution formula for the Tutte polynomial (that does not need the graph to be ordered)\;\n\n- and an expression of the Tutte polynomial usi ng only beta invariants of minors (that refines the above expressions).\n\ nI will mention that these expressions are all interrelated by the canonic al active bijection between spanning trees and orientations\, subject of a long-term joint work with Michel Las Vergnas. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/f75a99d5-2aca-4d95-befd-aa7f2efc21d6 END:VEVENT BEGIN:VEVENT SUMMARY:Cristophe Paul\, «Retour sur WG 2018» DTSTART;VALUE=DATE-TIME:20180712T081500Z DTEND;VALUE=DATE-TIME:20180712T091500Z DTSTAMP;VALUE=DATE-TIME:20180711T173959Z UID:970c08a6-7ecf-4238-8141-10728036b36b SEQUENCE:0 CREATED;VALUE=DATE-TIME:20180711T173959Z DESCRIPTION:Présentation de quelques articles de WG 2018. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION: URL:https://info-web.lirmm.fr/collorg/970c08a6-7ecf-4238-8141-10728036b36b END:VEVENT BEGIN:VEVENT SUMMARY:Jorgen Bang-Jensen\, «Disjoint paths in tournaments and semicompl ete digraphs» DTSTART;VALUE=DATE-TIME:20160901T080000Z DTEND;VALUE=DATE-TIME:20160901T090000Z DTSTAMP;VALUE=DATE-TIME:20160825T145008Z UID:5c59b6d8-039a-406a-a265-a7e93fdbd7d3 SEQUENCE:0 CREATED;VALUE=DATE-TIME:20160825T145008Z DESCRIPTION:A digraph is semicomplete if it has no pair of non-adjacent ve rtices.\nA tournament is a semicomplete digraph with no directed 2-cycles. \nTournaments form the most well studied class of directed graphs and a\nl ot is known about their structure\, ranging from very basic things you can \nteach a 1.st year student to extremely complicated things that take 100\ npages or more to prove. I will survey some important results on connec-\n tivity and give the main details of a recent proof\, due to Pokrovskiy\, t hat\nevery 452k-strong tournament T is k linked\, that is\, for every choi ce of 2k\nvertices {x 1 \, x 2 \, . . . \, x k \, y 1 \, y 2 \, . . . \, y k } there exist disjoint paths P 1 \, P 2 \, . . . \, P k\nin T so that P i is from x i to y i . Pokrovskiys beautiful proof of this result\nuses a very nice structural lemma which applies to all tournaments. If\nthere is time\, I will also say something more about the relation between\nsemicom plete digraphs and tournaments. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/5c59b6d8-039a-406a-a265-a7e93fdbd7d3 END:VEVENT BEGIN:VEVENT SUMMARY:Vinicius Fernandes dos Santos\, «Characterization\, probe and san dwich problems on a generalization of threshold graphs» DTSTART;VALUE=DATE-TIME:20180927T080000Z DTEND;VALUE=DATE-TIME:20180927T090000Z DTSTAMP;VALUE=DATE-TIME:20180831T072814Z UID:f264501b-8b42-4dd9-b8c4-3cad59217ea4 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20180831T072814Z DESCRIPTION:A cograph is a graph without induced paths of size 4. A graph G is (k\,l) if its vertex set can be partitioned into at most k independen t sets and l cliques. Cographs-(k\,l) have been studied on the literature\ , but no structural characterization is was known\, except for cographs-(1 \,1)\, i.e threshold graphs. In this talk\, we present a structural charac terization for cographs-(2\, 1). We show some applications of this charact erization on two generalizations of the recognition problem\, namely the r ecognition of probe cographs-(2\,1) and the sandwich problem.\n\nJoint wor k with Fernanda Couto\, Luerbio Faria\, Sylvain Gravier and Sulamita Klein . LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/f264501b-8b42-4dd9-b8c4-3cad59217ea4 END:VEVENT BEGIN:VEVENT SUMMARY:Julien Baste\, «Problèmes de connectivité paramétrés par la t reewidth» DTSTART;VALUE=DATE-TIME:20141023T080000Z DTEND;VALUE=DATE-TIME:20141023T090000Z DTSTAMP;VALUE=DATE-TIME:20141016T120306Z UID:54e39c47-feeb-4473-b1dc-9e67975b16c7 SEQUENCE:0 CREATED;VALUE=DATE-TIME:20141016T120306Z DESCRIPTION:Dans cette présentation nous nous intéresserons à des probl èmes "de connexité" paramétrés par la treewidth. Tous les problèmes évoqués sont solubles par des algorithmes classiques en un temps 2^{O(tw log tw)}*poly(n). Nous nous intéresserons à l'algorithme de Cut&Count [ 1] réduisant ce temps de calcul pour la plupart de ces problèmes à un t emps 2^{O(tw)}*poly(n) dans les graphes généraux puis examinerons les li ens et les différences de complexité de ces problèmes de connexité ent re les graphes généraux et les graphes planaires.\n\n[1] Marek Cygan\, J esper Nederlof\, Marcin Pilipczuk\, Michal Pilipczuk\, Johan M. M. van Roo ij\, Jakub Onufry Wojtaszczyk: Solving connectivity problems parameterized by treewidth in single exponential time. FOCS 2011.\n\nTravail en commun avec Ignasi Sau. LAST-MODIFIED;VALUE=DATE-TIME:20191104T080840Z LOCATION:E.3.23\, LIRMM URL:https://info-web.lirmm.fr/collorg/54e39c47-feeb-4473-b1dc-9e67975b16c7 END:VEVENT BEGIN:VEVENT SUMMARY:Marc Heinrich\, «Counting independent sets in strongly orderable graphs» DTSTART;VALUE=DATE-TIME:20191219T090000Z DTEND;VALUE=DATE-TIME:20191219T100000Z DTSTAMP;VALUE=DATE-TIME:20191208T211138Z UID:ebf19964-4573-4450-b1d4-470395359f9c SEQUENCE:0 CREATED;VALUE=DATE-TIME:20191208T211138Z DESCRIPTION:We are interested in counting problems which consists in compu ting the number of solutions to a given instance of the problem. This kind of question has strong connexions\, in particular in the case of independ ent sets\, with problems from statistical physics and what is called the h ard core distribution. As many counting problems\, counting exactly the nu mber of independent sets of a graphs is difficult (i.e.\, #P-complete) eve n on bipartite graphs\, and even difficult to approximate for general grap hs. On the other hands\, it was shown to be polynomial time solvable for m ore restricted classes of graphs such as chordal graphs\, cographs or mono tone bipartite graphs. We show that the number of independent sets can als o be computed in polynomial time for strongly orderable graphs which is a super-class of chordal bipartite and strongly chordal graphs.\n\nThis is j oint work with Haiko Muller. LAST-MODIFIED;VALUE=DATE-TIME:20191218T090103Z LOCATION:E3.23 URL:https://info-web.lirmm.fr/collorg/ebf19964-4573-4450-b1d4-470395359f9c END:VEVENT BEGIN:VEVENT SUMMARY:Florent Tallerie\, «Réalisations polyédrales de surfaces de tra nslation» DTSTART;VALUE=DATE-TIME:20250925T080000Z DTEND;VALUE=DATE-TIME:20250925T090000Z DTSTAMP;VALUE=DATE-TIME:20250905T082853Z UID:9d9828c4-9005-40d4-8819-55b7119e229b SEQUENCE:2 CREATED;VALUE=DATE-TIME:20250905T082853Z DESCRIPTION:Considérons la surface abstraite obtenue par recollement des côtés horizontaux d'une feuille de papier rectangulaire. Il est facile d 'obtenir une réalisation de cette surface : il suffit de courber la feuil le de manière à identifier les deux côtés horizontaux. On peut le fair e\, par exemple\, de manière à obtenir un cylindre droit à section circ ulaire\, ou encore de manière à obtenir un prisme droit à section polyg onale si l'on s'autorise à introduire des plis. Dans cet exposé\, nous n ous intéresserons uniquement aux réalisations sous forme de polyèdre. C ependant\, si l'on veut réaliser un tore plat\, c'est-à-dire la surface obtenue en recollant également les côtés verticaux\, la construction es t bien moins claire. Une méthode\, due à Burago et Zalgaller\, permet de réaliser géométriquement n'importe quel recollement de polygones. \nCo nsidérons maintenant l'aspect uniforme de telles réalisations : est-il p ossible\, étant donnée une famille de surfaces\, de construire une trian gulation fixée qui réalisent tous les éléments de cette famille ? Je r épondrai par l'affirmative dans le cas de la famille des tores plats. Nou s nous intéresserons ensuite à la famille des surfaces obtenues par reco llement de 3 parallélogrammes formant un L\, surfaces qui forment une fam ille importante de surfaces appelée H(2). LAST-MODIFIED;VALUE=DATE-TIME:20250924T080103Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/9d9828c4-9005-40d4-8819-55b7119e229b END:VEVENT BEGIN:VEVENT SUMMARY:Giannos Stamoulis\, «Parameterized Algorithms for Vertex Deletion to Minor-closed Graph Classes» DTSTART;VALUE=DATE-TIME:20210415T080000Z DTEND;VALUE=DATE-TIME:20210415T090000Z DTSTAMP;VALUE=DATE-TIME:20210324T085959Z UID:11ed6817-e8b1-44d3-96f7-94605afd8fee SEQUENCE:5 CREATED;VALUE=DATE-TIME:20210324T085959Z DESCRIPTION:Let ${\\cal G}$ be a minor-closed graph class. We provide an a lgorithm that\, given a graph $G$ on $n$ vertices\, runs in time $2^{{\\s f poly}(k)}\\cdot n^3$ and either returns a set $S$ such that $G\\setmin us S$ belongs to ${\\cal G}$\, or reports that such a et does not exist. Here ${\\sf poly}$ is a polynomial function whose degree depends on the ma ximum size of a minor-obstruction of ${\\cal G}.$ In the special case wher e ${\\cal G}$ excludes some apex graph as a minor\, we give an alternativ e algorithm running in $2^{{\\sf poly}(k)}\\cdot n^2$-time.\n\nJoint wor k with Ignasi Sau and Dimitrios M. Thilikos LAST-MODIFIED;VALUE=DATE-TIME:20210414T080102Z LOCATION:https://bbb.lirmm.fr/b/dim-ajj-ddd URL:https://info-web.lirmm.fr/collorg/11ed6817-e8b1-44d3-96f7-94605afd8fee END:VEVENT BEGIN:VEVENT SUMMARY:Hoang La\, «Déchargement assisté par ordinateur : application à la coloration à distance 2» DTSTART;VALUE=DATE-TIME:20201217T090000Z DTEND;VALUE=DATE-TIME:20201217T100000Z DTSTAMP;VALUE=DATE-TIME:20201123T121745Z UID:0b90f4aa-f721-4aa1-b2f1-d09f9b056697 SEQUENCE:5 CREATED;VALUE=DATE-TIME:20201123T121745Z DESCRIPTION:On ne considère ici que des graphes simples sans boucles. Une $k$-coloration propre de $G = (V\, E)$ est une coloration des sommets de $G$ avec des couleurs de 1 à $k$ telle que deux sommets adjacents reçoiv ent des couleurs différentes. Une $k$-coloration des sommets à distance 2\, est une $k$-coloration propre telle que toute paire de sommets à dist ance au plus 2 reçoivent des couleurs différentes. Le nombre chromatique à distance 2 de $G$\, noté $χ^2(G)$\, est le plus petit entier $k$ tel que $G$ admet une $k$-coloration à distance 2. Dans le cas général\, $ χ^2(G) ≤ ∆^2(G)$ où $∆(G)$ est le degré maximum du graphe. Un exe mple atteignant la borne est le graphe de Petersen. L’étude des graphes épars est devenu un sujet de recherche actif\, motivé par le passage de la borne quadratique à $χ^2(G) ≤ ∆(G) + c$ pour une petite constant e $c$.\nOn s’intéresse à la coloration à distance 2 des graphes plana ires subcubiques. Plus précisément\, on montre le résultat suivant : si $G$ est un graphe planaire subcubique de maille au moins 8\, alors $χ^2( G) ≤ 6$. Ce résultat améliore celui de Cranston et Kim pour les graphe s planaires subcubiques de maille 9 [D. Cranston and S.-J. Kim\, List-colo ring the square of subcubic graph\, J. Graph Theory 57(1) (2008)\, 65–87 ].\nLa preuve est faite par déchargement. L’assistance par ordinateur j oue un rôle crucial dans la vérification des charges et l’identificati on des configurations réductibles. L’intérêt de cette méthode est la possibilité d’améliorer la borne sur la maille des résultats existan ts de la forme : si $G$ est un graphe planaire de degré maximum $∆$ et de maille au moins $G$ alors $χ^2(G) ≤ ∆+c$ pour une petite constante $c$. L’encodage utilisé pour représenter les sous-graphes et l’algo rithme de déchargement sont généralisables à d’autres colorations av ec procédure de déchargement locale sur les graphes planaires.\n\n\nTrav ail conjoint avec Petru Valicov\n\nTéléseminaire: [[https://bbb.lirmm.fr /b/dim-ajj-ddd]] LAST-MODIFIED;VALUE=DATE-TIME:20201216T090103Z LOCATION:Téléseminaire: https://bbb.lirmm.fr/b/dim-ajj-ddd URL:https://info-web.lirmm.fr/collorg/0b90f4aa-f721-4aa1-b2f1-d09f9b056697 END:VEVENT BEGIN:VEVENT SUMMARY:William Lochet\, «A polynomial time algorithm for the k-disjoint shortest path problem» DTSTART;VALUE=DATE-TIME:20210121T090000Z DTEND;VALUE=DATE-TIME:20210121T100000Z DTSTAMP;VALUE=DATE-TIME:20210108T103532Z UID:1449a387-7c57-444a-9031-9d7c3bee5bb9 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20210108T103532Z DESCRIPTION:The disjoint paths problem is a fundamental problem in\nalgori thmic graph theory. For a given graph $G$ and a set of $k$ pairs\nof termi nals in $G$\, it asks for the existence of $k$ vertex-disjoint\npaths conn ecting each pair of terminals. Very famously\, Robertson and\nSeymour prov ed the existence of a $n^3$ algorithm for any fixed $k$ in\n1995 as part o f the Graph Minor project. In this talk\, we focus on the\nversion of this problem where all the paths are required to be\nshortest paths. This was first introduced as the disjoint shortest\npaths problem by Eilam-Tzoreff in 1998 where she proved that the case\n$k = 2$ admits a polynomial time a lgorithm. She also asked for the\nexistence of a polynomial time algorithm for any fixed $k$\, a question\nwhich remained open even for the case $k = 3$. The goal of this talk\nis to prove that\, for any fixed $k$\, there exists a $n^{f(k)}$\nalgorithm for the $k$-disjoint shortest paths problem \, answering\nEilam-Tzoreff's question. LAST-MODIFIED;VALUE=DATE-TIME:20210120T090102Z LOCATION:Téléseminaire: https://bbb.lirmm.fr/b/dim-ajj-ddd URL:https://info-web.lirmm.fr/collorg/1449a387-7c57-444a-9031-9d7c3bee5bb9 END:VEVENT BEGIN:VEVENT SUMMARY:Mamadou Moustapha Kanté\, «Letter graphs: Characterisation\, rec ognition and relations with geometric grid classes of permutations» DTSTART;VALUE=DATE-TIME:20211216T090000Z DTEND;VALUE=DATE-TIME:20211216T100000Z DTSTAMP;VALUE=DATE-TIME:20211019T113426Z UID:ea076496-7219-416b-aa44-d6f15ee18d3f SEQUENCE:4 CREATED;VALUE=DATE-TIME:20211019T113426Z DESCRIPTION:We will present the graph parameter lettericity\, which roughl y tells how a graph looks like a word on a fixed alphabet and give some ex amples of bounded/unvounded lettericity. Letter graphs enjoy nice properti es\, in particular they are well-quasi-ordered under induced subgraphs. We propose a combinatorial characterisation and propose from this an MS-defi nability of graphs of lettericity k\, for fixed k\, and a bound on the num ber of vertices of an obstruction. The MS-definability implies also a cubi c FPT-recognition algorithm. In a second step we introduce the notion of geometric grid permutations\, which are permutations that can be mapped on a grid and that enjoy very nice properties (well-quasi-order\, algebraici ty\, etc.). We show that a geometric permutation class has bounded griddab ility iff its permutations graphs have bounded lettericity. \n\nThis is a joint work with B. Alecu\, R. Ferguson\, V. Lozin\, V. Vatter and V. Zamar aev. LAST-MODIFIED;VALUE=DATE-TIME:20211215T090102Z LOCATION:https://bbb.lirmm.fr/b/dim-ajj-ddd URL:https://info-web.lirmm.fr/collorg/ea076496-7219-416b-aa44-d6f15ee18d3f END:VEVENT BEGIN:VEVENT SUMMARY:Christophe Paul\, «L’algorithme de reconnaissance des graphes d e cercle était linéaire» DTSTART;VALUE=DATE-TIME:20251016T080000Z DTEND;VALUE=DATE-TIME:20251016T090000Z DTSTAMP;VALUE=DATE-TIME:20250918T080012Z UID:256525c6-ad26-4857-803f-fa112d0d7646 SEQUENCE:3 CREATED;VALUE=DATE-TIME:20250918T080012Z DESCRIPTION:Un graphe de cercle est le graphe d’intersection de cordes i nscrites dans un\ncercle. En 2014\, avec D. Corneil\, E. Gioan et M. Tedde r\, nous avons publié un\nalgorithme quasi-linéaire pour la reconnaissan ce des graphes de cercle. Comme\nses prédécesseurs\, cet algorithme repo se sur le calcul de la décomposition en coupes.\nEn utilisant un ordre Le xBFS\, nous avions montré comment la décomposition en coupes\npouvait ê tre calculer en temps quasi-linéaire. L’obstacle à une complexité lin éaire était\nl’utilisation de l’union-find pour mettre à jour l’a rbre de décomposition lors de l’insertion\nd’un sommet. Même dans le cas restreint des graphes de cercle\, nous n’avions pas\nréussi à lev er cet obstacle. L’existence d’un algorithme linéaire pour la reconna issance\ndes graphes de cercle restait une question ouverte. Avec I. Rutte r (Univ. Passau)\, nous\nmontrons que c’est possible en utilisant des ar bres-PC. LAST-MODIFIED;VALUE=DATE-TIME:20251015T080103Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/256525c6-ad26-4857-803f-fa112d0d7646 END:VEVENT BEGIN:VEVENT SUMMARY:Dimitrios Thilikos\, «Θ-logic and Algorithmic meta-theorems: Whe n big kingdoms fall from within» DTSTART;VALUE=DATE-TIME:20220113T090000Z DTEND;VALUE=DATE-TIME:20220113T100000Z DTSTAMP;VALUE=DATE-TIME:20211206T143953Z UID:345b436c-3a41-415f-9396-19b000292b06 SEQUENCE:8 CREATED;VALUE=DATE-TIME:20211206T143953Z DESCRIPTION:We introduce a novel model-theoretic framework inspired from g raph modification and based on the interplay between model theory and algo rithmic graph minors. We propose a new //compound logic// operating with two types of sentences\, expressing graph modification: the //modulator s entence//\, defining some property of the modified part of the graph\, a nd the //target sentence//\, defining some property of the resulting grap h. In our framework\, modulator sentences are in monadic second-order log ic and have models of bounded treewidth\, while target sentences express first-order logic properties along with minor-exclusion. Our logic capt ures problems that are not definable in first-order logic and\, moreover \, may have instances of unbounded treewidth. Also\, it permits the model ing of wide families of problems involving vertex/edge removals\, alterna tive modulator measures (such as elimination distance or ${\\cal G}$-treew idth)\, multistage modifications\, and various cut problems. Our main resu lt is that\, for this compound logic\, model checking can be done in quad ratic time. This algorithmic meta-theorem encompasses\, unifies\, and exte nds all known meta-algorithmic results on minor-closed graph classes. Mor eover\, all derived algorithms are constructive and this\, as a byproduct \, extends the constructibility horizon of the algorithmic applications o f the Graph Minors theorem of Robertson and Seymour. The proposed logic c an be seen as a general framework to capitalize on the potential of the // irrelevant vertex technique//. It gives a way to deal with problem instanc es of unbounded treewidth\, for which Courcelle's theorem does not apply.\ n\nJoint work with Fedor V. Fomin\, Petr A. Golovach\, Ignasi Sau\, and Gi annos Stamoulis LAST-MODIFIED;VALUE=DATE-TIME:20220112T090102Z LOCATION:https://bbb.lirmm.fr/b/dim-ajj-ddd URL:https://info-web.lirmm.fr/collorg/345b436c-3a41-415f-9396-19b000292b06 END:VEVENT BEGIN:VEVENT SUMMARY:Kenny Štorgel\, «Further Extensions of the Grötzsch Theorem» DTSTART;VALUE=DATE-TIME:20211021T080000Z DTEND;VALUE=DATE-TIME:20211021T090000Z DTSTAMP;VALUE=DATE-TIME:20211008T110425Z UID:026e3518-8d70-4bb3-a830-52478c92b8a4 SEQUENCE:4 CREATED;VALUE=DATE-TIME:20211008T110425Z DESCRIPTION:The Grötzsch Theorem states that every triangle-free planar g raph $G$ admits a proper $3$-coloring\, i.e. a coloring of the vertices of $G$ with three colors such that adjacent vertices are assigned distinct c olors. However\, we may also allow triangles in general planar graphs and still retain $3$-colorability. Havel conjectured that a $3$-colorable plan ar graph may contain arbitrarily many triangles as long as they are suffic iently far apart. This conjecture was proved by Dvořák\, Kráľ\, and Th omas. On the other hand\, there are $3$-colorable planar graphs that may h ave close triangles (even incident). A result by Dross et al. states that every planar graph obtained as a subgraph of the medial graph of a biparti te plane graph is $3$-colorable. \nAs mentioned\, the Grötzsch Theorem ha s many generalizations\, although\, perhaps the most well-known is a resul t of Grünbaum and Aksenov\, giving $3$-colorability of planar graphs with at most three triangles\, which is in general best possible. A lot of att ention was also given to extending $3$-colorings of subgraphs of triangle- free planar graphs to the whole graph. In particular\, a result of Aksenov \, Borodin\, and Glebov states that we can precolor any two non-adjacent v ertices in a triangle-free planar graph and retain $3$-colorability. Furth ermore\, several other results exist which deal with precolorings of a fac e of certain length in a triangle-free planar graph.\nIn this talk\, we wi ll present the above-mentioned results and provide further extensions of t he Grötzsch Theorem by considering $3$-colorings of planar graphs with at most one triangle. In particular\, we show that a precoloring of any two non-adjacent vertices and a precoloring of a face of length at most $4$ ca n be extended to a $3$-coloring of the whole graph. Additionally\, we show that for every vertex of degree at most $3$ in a planar graph with at mos t one triangle\, a precoloring of its neighborhood with the same color ext ends to a $3$-coloring of the whole graph. The latter result yields an aff irmative answer to a conjecture on adynamic coloring. LAST-MODIFIED;VALUE=DATE-TIME:20211020T080103Z LOCATION:BAT4 l Séminaire LIRMM - RDC Entrée URL:https://info-web.lirmm.fr/collorg/026e3518-8d70-4bb3-a830-52478c92b8a4 END:VEVENT BEGIN:VEVENT SUMMARY:Ioan Todinca\, «A Meta-Theorem for Distributed Certification» DTSTART;VALUE=DATE-TIME:20220217T090000Z DTEND;VALUE=DATE-TIME:20220217T100000Z DTSTAMP;VALUE=DATE-TIME:20211211T030129Z UID:986725cb-a608-44c9-add8-3ad62ad807dd SEQUENCE:6 CREATED;VALUE=DATE-TIME:20211211T030129Z DESCRIPTION:Distributed certification\, whether it be proof-labeling schem es\, locally checkable proofs\, etc.\, deals with the issue of certifying the legality of a distributed system with respect to a given boolean predi cate. A certificate is assigned to each process in the system by a non-tru stable oracle\, and the processes are in charge of verifying these certifi cates\, so that two properties are satisfied: completeness\, i.e.\, for ev ery legal instance\, there is a certificate assignment leading all process es to accept\, and soundness\, i.e.\, for every illegal instance\, and for every certificate assignment\, at least one process rejects. The verifica tion of the certificates must be fast\, and the certificates themselves mu st be small. A large quantity of results have been produced in this framew ork\, each aiming at designing a distributed certification mechanism for s pecific boolean predicates. This paper presents a "meta-theorem"\, applyin g to many boolean predicates at once. Specifically\, we prove that\, for e very boolean predicate on graphs definable in the monadic second-order (MS O) logic of graphs\, there exists a distributed certification mechanism us ing certificates on $O(\\log^2n)$ bits in n-node graphs of bounded treewid th\, with a verification protocol involving a single round of communicatio n between neighbors. LAST-MODIFIED;VALUE=DATE-TIME:20220216T090102Z LOCATION:https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/986725cb-a608-44c9-add8-3ad62ad807dd END:VEVENT BEGIN:VEVENT SUMMARY:Hoang La\, «Boolean dimension of boolean lattices» DTSTART;VALUE=DATE-TIME:20230427T080000Z DTEND;VALUE=DATE-TIME:20230427T090000Z DTSTAMP;VALUE=DATE-TIME:20230407T163600Z UID:70bce9cd-2feb-4ffa-95d2-398c5cc81f32 SEQUENCE:0 CREATED;VALUE=DATE-TIME:20230407T163600Z DESCRIPTION:Dimension is often defined as a measure of complexity of a pos et. In that sense\, boolean dimension is an even more compact way of encod ing a poset. Moreover\, behind each directed graph G\, there exists a corr esponding poset such that its boolean realizer gives a reachability labeli ng scheme for G. In an effort to better understand this measure\, we study the boolean dimension for boolean lattices where the question of the equa lity of its Dushnik-Miller dimension and boolean dimension is open. We ans wer this question in the negative and provide lower and upper bounds for b oolean dimension of boolean lattices. LAST-MODIFIED;VALUE=DATE-TIME:20230426T080103Z LOCATION:https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/70bce9cd-2feb-4ffa-95d2-398c5cc81f32 END:VEVENT BEGIN:VEVENT SUMMARY:Tuukka Korhonen\, «A Single-Exponential Time 2-Approximation Algo rithm for Treewidth» DTSTART;VALUE=DATE-TIME:20220120T090000Z DTEND;VALUE=DATE-TIME:20220120T100000Z DTSTAMP;VALUE=DATE-TIME:20211123T083506Z UID:d346368b-9731-4f5c-9069-c7a590b76eae SEQUENCE:4 CREATED;VALUE=DATE-TIME:20211123T083506Z DESCRIPTION:We give an algorithm\, that given an $n$-vertex graph $G$ and an integer $k$\, in time $2^{O(k)} n$ either outputs a tree decomposition of $G$ of width at most $2k+1$ or determines that the treewidth of G is la rger than $k$. This is the first 2-approximation algorithm for treewidth t hat is faster than the known exact algorithms. In particular\, our algorit hm improves upon both the previous best approximation ratio of 5 in time $ 2^{O(k)} n$ and the previous best approximation ratio of 3 in time $2^{O(k )} n^{O(1)}$\, both given by Bodlaender et al. [SICOMP 2016]. Our algorith m is based on a local improvement method adapted from a proof of Bellenbau m and Diestel [Comb. Probab. Comput. 2002]. LAST-MODIFIED;VALUE=DATE-TIME:20220119T090102Z LOCATION:https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/d346368b-9731-4f5c-9069-c7a590b76eae END:VEVENT BEGIN:VEVENT SUMMARY:Marin Bougeret\, «On the complexity of computing Maximum Minimal Blocking Sets» DTSTART;VALUE=DATE-TIME:20210318T090000Z DTEND;VALUE=DATE-TIME:20210325T100000Z DTSTAMP;VALUE=DATE-TIME:20210125T145934Z UID:b0bb569e-d89c-42c1-bc91-af39c84ccc0f SEQUENCE:4 CREATED;VALUE=DATE-TIME:20210125T145934Z DESCRIPTION:A blocking set in a graph $G$ is a subset of vertices that int ersects every maximum independent set of $G$. Let 𝗆𝗆𝖻𝗌($G$) be the size of a maximum (inclusion-wise) minimal blocking set of $G$. This parameter has recently played an important role in the kernelization of Ve rtex Cover parameterized by the distance to a graph class ${\\cal F}$. Ind eed\, it turns out that the existence of a polynomial kernel for this prob lem is closely related to the property that 𝗆𝗆𝖻𝗌$({\\cal F})=s up_{G∈F}$𝗆𝗆𝖻𝗌$(G)$ is bounded by a constant\, and thus sever al recent results focused on determining 𝗆𝗆𝖻𝗌$(F)$ for differe nt classes $F$. We consider the parameterized complexity of computing 𝗆 𝗆𝖻𝗌 under various parameterizations\, such as the size of a maxim um independent set of the input graph and the natural parameter. We provid e a panorama of the complexity of computing both 𝗆𝗆𝖻𝗌 and 𝗆 𝗆𝗁𝗌\, which is the size of a maximum minimal hitting set of a hyp ergraph\, a closely related parameter. Finally\, we consider the problem o f computing 𝗆𝗆𝖻𝗌 parameterized by treewidth\, especially relev ant\nin the context of kernelization. Given the "counting" nature of 𝗆 𝗆𝖻𝗌\, it does not seem to be expressible in monadic second-order logic\, hence its tractability does not follow from Courcelle's theorem. O ur main technical contribution is a fixed-parameter tractable algorithm fo r this problem. LAST-MODIFIED;VALUE=DATE-TIME:20210317T090103Z LOCATION:Téléseminaire: https://bbb.lirmm.fr/b/dim-ajj-ddd URL:https://info-web.lirmm.fr/collorg/b0bb569e-d89c-42c1-bc91-af39c84ccc0f END:VEVENT BEGIN:VEVENT SUMMARY:Dimitrios M. Thilikos\, «Bounding the Obstructions for Apices of Minor-closed Graph Classes» DTSTART;VALUE=DATE-TIME:20210408T080000Z DTEND;VALUE=DATE-TIME:20210408T090000Z DTSTAMP;VALUE=DATE-TIME:20210324T084006Z UID:0b10988e-fbb3-438d-9537-e5a2ab58e0de SEQUENCE:25 CREATED;VALUE=DATE-TIME:20210324T084006Z DESCRIPTION:Let ${\\cal G}$ be a minor-closed graph class. We say that a g raph $G$ is a //$k$-apex// of ${\\cal G}$ if $G$ contains a set $S$ of at most $k$ vertices such that $G\\setminus S$ belongs to ${\\cal G}.$ We den ote by ${\\cal A}_k ({\\cal G})$ the graph class containining the graphs t hat are $k$-apices of ${\\cal G}.$ We prove that every graph in the obstru ction set of ${\\cal A}_k ({\\cal G})\, $i.e.\, the minor-minimal set of g raphs not belonging to ${\\cal A}_k ({\\cal G})\,$ has size at most $2^{2^ {2^{2^{poly(k)}}}}\,$ where ${poly}$ is a polynomial function whose degree depends on the size of the minor-obstructions of ${\\cal G}.$\n\n\nJoint work with Ignasi Sau and Giannos Stamoulis LAST-MODIFIED;VALUE=DATE-TIME:20210407T080103Z LOCATION:https://bbb.lirmm.fr/b/dim-ajj-ddd URL:https://info-web.lirmm.fr/collorg/0b10988e-fbb3-438d-9537-e5a2ab58e0de END:VEVENT BEGIN:VEVENT SUMMARY:Archontia C. Giannopoulou\, «Excluding a Planar Matching Minor in Bipartite Graphs» DTSTART;VALUE=DATE-TIME:20210128T090000Z DTEND;VALUE=DATE-TIME:20210128T100000Z DTSTAMP;VALUE=DATE-TIME:20210108T101955Z UID:15404443-7d41-463a-a5b6-baa2a94f9f8e SEQUENCE:6 CREATED;VALUE=DATE-TIME:20210108T101955Z DESCRIPTION:A matching minor of a graph G with a perfect matching is a gra ph H obtained from a subgraph H' of G\, where G-H' has a perfect matching\ , by repeatedly contracting both edges incident with some vertex of degree two. We generalise basic ideas from the graph minor series by Robertson a nd Seymour to the setting of bipartite graphs with perfect matchings. In d oing so we show that every bipartite\, planar\, and matching covered graph has the Erdős-Pósa property for matching minors.\nWe describe an algori thm for a matching version of the disjoint paths problem on bipartite grap hs of bounded perfect matching width. Finally\, by combining these results \, we show that the problem of deciding whether a bipartite graph with a p erfect matching contains a fixed bipartite\, planar\, and matching covered graph H as a matching minor is polynomial time solvable. LAST-MODIFIED;VALUE=DATE-TIME:20210324T120507Z LOCATION:Téléseminaire: https://bbb.lirmm.fr/b/dim-ajj-ddd URL:https://info-web.lirmm.fr/collorg/15404443-7d41-463a-a5b6-baa2a94f9f8e END:VEVENT BEGIN:VEVENT SUMMARY:Sebastian Wiederrecht\, «A matching theoretic approach to structu ral digraph theory» DTSTART;VALUE=DATE-TIME:20210304T090000Z DTEND;VALUE=DATE-TIME:20210304T100000Z DTSTAMP;VALUE=DATE-TIME:20210113T145939Z UID:b9d0e67c-d403-4e18-9837-95c6759c3f32 SEQUENCE:2 CREATED;VALUE=DATE-TIME:20210113T145939Z DESCRIPTION:The theory of butterfly minors in digraphs which is closelinke d to the notion of directed treewidth has become an active field of resear ch in the past years. Many great advancements have been made such as a dir ected version of the famous Grid Theorem and several other generalisations of great results from the Graph Minors Series of Robterson and Seymour. \ nHowever\, many of these results appear flawd when first encountered: The Erdős-Pósa property of butterfly minors does not appear to be linked to a topological property\, and the directed version of the Flat Wall is not actually flat. \nIn this talk we identify two possible reasons for these f laws and show how recent advancements in the area of structural matching t heory can be used\, by rethinking the way we handle butterfly minors and u navoidable infinite anti-chains of them\, to achieve much nicer results. LAST-MODIFIED;VALUE=DATE-TIME:20210324T120538Z LOCATION:Téléseminaire: https://bbb.lirmm.fr/b/dim-ajj-ddd URL:https://info-web.lirmm.fr/collorg/b9d0e67c-d403-4e18-9837-95c6759c3f32 END:VEVENT BEGIN:VEVENT SUMMARY:Ignasi Sau\, «Kernelization of Maximum Minimal Vertex Cover» DTSTART;VALUE=DATE-TIME:20210325T090000Z DTEND;VALUE=DATE-TIME:20210325T100000Z DTSTAMP;VALUE=DATE-TIME:20210125T150040Z UID:034e27d8-95bd-4738-a269-f14137d5a2a6 SEQUENCE:8 CREATED;VALUE=DATE-TIME:20210125T150040Z DESCRIPTION:In the **Maximum Minimal Vertex Cover** (MMVC) problem\, we a re given a graph $G$ and a positive integer $k$\, and the objective is to decide whether $G$ contains a minimal vertex cover of size at least $k$. T his problem has been considered in several articles in the last years. In this talk we focus on its kernelization\, which had been almost unexplored so far. We prove that MMVC does not admit polynomial kernels parameteriz ed by the size of a minimum vertex cover or of a maximum matching\, unless NP⊆coNP/poly. Motivated by a question of Boria et al. (Discret. Appl. Math. 2015) about the existence of subquadratic kernels for MMVC paramet erized by $k$\, we rule out their existence unless P=NP\, if we restrict the kernelization algorithms to apply only a type of natural reduction rul es that we call //large optimal preserving rules//. In particular\, these rules contain the typical reduction rules to obtain linear kernels for ** Vertex Cover**. On the positive side\, we provide subquadratic kernels on $H$-free graphs for several graphs $H$\, such as the bull\, the paw\, or t he cliques\, by making use of the Erdős-Hajnal property in order to find an appropriate decomposition. \n\n\nJoint work with Júlio Araújo\, Mari n Bougeret\, and Victor A. Campos. LAST-MODIFIED;VALUE=DATE-TIME:20210324T120647Z LOCATION:Téléseminaire: https://bbb.lirmm.fr/b/dim-ajj-ddd URL:https://info-web.lirmm.fr/collorg/034e27d8-95bd-4738-a269-f14137d5a2a6 END:VEVENT BEGIN:VEVENT SUMMARY:Mathieu Mari\, «A (2+ε)-Approximation Algorithm for Maximum Inde pendent Set of Rectangle» DTSTART;VALUE=DATE-TIME:20230413T080000Z DTEND;VALUE=DATE-TIME:20230413T090000Z DTSTAMP;VALUE=DATE-TIME:20230330T074641Z UID:c9f09ec1-0fa8-4f05-8f27-0d407c32dd5c SEQUENCE:2 CREATED;VALUE=DATE-TIME:20230330T074641Z DESCRIPTION:We study the Maximum Independent Set of Rectangles (MISR) prob lem\, where we are given a set of axis-parallel rectangles in the plane an d the goal is to select a subset of non-overlapping rectangles of maximum cardinality. In a recent breakthrough\, Mitchell obtained the first consta nt-factor approximation algorithm for MISR. His algorithm achieves an appr oximation ratio of 10 and it is based on a dynamic program that intuitivel y recursively partitions the input plane into special polygons called corn er-clipped rectangles (CCRs)\, without intersecting certain special horizo ntal line segments called fences. In this talk\, I will present a (2+ε)-a pproximation algorithm for MISR which is also based on a recursive partiti oning scheme. First\, we use a partition into a class of axis-parallel pol ygons with constant complexity each that are more general than CCRs. This allows us to provide an arguably simpler analysis and at the same time alr eady improves the approximation ratio to 4. Then\, using a more elaborate charging scheme and a recursive partitioning into general axis-parallel po lygons with constant complexity\, we improve our approximation ratio to 2+ ε. In particular\, we construct a recursive partitioning based on more ge neral fences which can be sequences of up to O(1/ε) line segments each. T his partitioning routine and our other new ideas may be useful for future work towards a PTAS for MISR. At the end of the talk\, I will present a bu nch of future research directions related to the problem.\n\nThis is a joi nt work with Waldo Gálvez\, Arindam Khan\, Tobias Mömke\,\nMadhusudhan R eddy and Andreas Wiese. LAST-MODIFIED;VALUE=DATE-TIME:20230412T080102Z LOCATION:E.3.23 Bâtiment 4 LIRMM\, https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/c9f09ec1-0fa8-4f05-8f27-0d407c32dd5c END:VEVENT BEGIN:VEVENT SUMMARY:Fedor V. Fomin\, «Paths\, cycles and beyond» DTSTART;VALUE=DATE-TIME:20210624T080000Z DTEND;VALUE=DATE-TIME:20210624T090000Z DTSTAMP;VALUE=DATE-TIME:20210426T073845Z UID:8a768e88-8a40-44c2-bd2b-0dcdd3020ede SEQUENCE:5 CREATED;VALUE=DATE-TIME:20210426T073845Z DESCRIPTION:I will speak about old and new parameterized algorithms for fi nding long paths and cycles in graphs. In particular\, we discuss problems of finding paths and cycles whose lengths are beyond some ``trivial'' bou nds. LAST-MODIFIED;VALUE=DATE-TIME:20210623T080102Z LOCATION:Téléseminaire: https://bbb.lirmm.fr/b/dim-ajj-ddd URL:https://info-web.lirmm.fr/collorg/8a768e88-8a40-44c2-bd2b-0dcdd3020ede END:VEVENT BEGIN:VEVENT SUMMARY:Laure Morelle\, «An introduction to odd-minors» DTSTART;VALUE=DATE-TIME:20231012T080000Z DTEND;VALUE=DATE-TIME:20231012T090000Z DTSTAMP;VALUE=DATE-TIME:20230928T073610Z UID:572604ed-e4ca-4dcd-b400-b8da1955d6c6 SEQUENCE:3 CREATED;VALUE=DATE-TIME:20230928T073610Z DESCRIPTION:Odd-minors\, which are essentially minors preserving the parit y of\ncycles\, are relatively unknown but would gain to be more famous due to\ntheir possible applications to coloring\, parameterized complexity\, and\nstructural graph theory\, to cite just a few. In particular\,\nodd-mi nor-closed graph classes generalize both minor-closed graph\nclasses and b ipartite graphs. We present here known results and\nconjectures related to odd-minors\, and revisit a graph width parameter\nthat we dub bipartite t reewidth\, that seems closely related to odd-minors. LAST-MODIFIED;VALUE=DATE-TIME:20231011T080102Z LOCATION:E.3.24 Bâtiment 4 LIRMM URL:https://info-web.lirmm.fr/collorg/572604ed-e4ca-4dcd-b400-b8da1955d6c6 END:VEVENT BEGIN:VEVENT SUMMARY:François Pirot\, «Complexity thresholds for fractional distribut ed colouring» DTSTART;VALUE=DATE-TIME:20210218T090000Z DTEND;VALUE=DATE-TIME:20210218T100000Z DTSTAMP;VALUE=DATE-TIME:20210108T111311Z UID:3acacad6-809a-45be-bc79-544dc746114b SEQUENCE:4 CREATED;VALUE=DATE-TIME:20210108T111311Z DESCRIPTION:In the domain of distributed algorithms\, the complexity is co nsidered in terms of rounds\, during which the nodes of a graph can exchan ge data with their neighbours. Moreover\, in the LOCAL model\, the nodes a re assumed to have infinite computational power\, so any problem can be so lved within D rounds\, if D is the diameter of the graph. When considering distributed colourings of graphs of fixed maximum degree Δ on n vertices \, an interesting complexity threshold appears. There exists a determinist ic distributed algorithm for finding a colouring with Δ+1 colours within O(log* n) rounds. If the graph is neither complete nor an odd cycle\, Broo ks' Theorem tells us that there exists a colouring with Δ colours. It tur ns out that any distributed algorithm constructing such a colouring requir es Ω(log n) rounds if it is deterministic\, or Ω(log log n) rounds if it is probabilistic.\n\nIn this talk\, I will present a similar sharp thresh old for the complexity of distributed fractional colourings of graphs of f ixed maximum degree\, and of d-dimensional grids. Finally\, I will present a distributed algorithm for constructing a fractional colouring of weight 2+ε of graphs of maximum average degree 2+ε' and sufficiently large gir th\, within O(log n) rounds.\n\nJoint work with Nicolas Bousquet and Louis Esperet. LAST-MODIFIED;VALUE=DATE-TIME:20210324T120716Z LOCATION:Téléseminaire: https://bbb.lirmm.fr/b/dim-ajj-ddd URL:https://info-web.lirmm.fr/collorg/3acacad6-809a-45be-bc79-544dc746114b END:VEVENT BEGIN:VEVENT SUMMARY:Stéphane Bessy\, «Directed tree-width for dummies» DTSTART;VALUE=DATE-TIME:20210527T080000Z DTEND;VALUE=DATE-TIME:20210527T090000Z DTSTAMP;VALUE=DATE-TIME:20210426T073944Z UID:519b510a-3101-4c9f-8f45-382d877025b7 SEQUENCE:3 CREATED;VALUE=DATE-TIME:20210426T073944Z DESCRIPTION:Un article récent de R. Steiner utilise pour la première foi s\, il me semble\, la 'directed tree-width' et le 'directed flat wall theo rem' pour prouver un résultat structurelle de théorie des graphes orient és. Ayant lu attentivement le papier (...) et trouvé la méthode très élégante et novatrice\, j'essayerai de faire un point sur les concepts e t résultats existants sur la directed tree-width et d'exposer les résult ats de R. Steiner. LAST-MODIFIED;VALUE=DATE-TIME:20210526T080103Z LOCATION:Téléseminaire: https://bbb.lirmm.fr/b/dim-ajj-ddd URL:https://info-web.lirmm.fr/collorg/519b510a-3101-4c9f-8f45-382d877025b7 END:VEVENT BEGIN:VEVENT SUMMARY:Sang-Il Oum (엄상일)\, «Obstructions for matroids of path-widt h at most k and graphs of linear rank-width at most k» DTSTART;VALUE=DATE-TIME:20211104T090000Z DTEND;VALUE=DATE-TIME:20211104T100000Z DTSTAMP;VALUE=DATE-TIME:20211018T044108Z UID:3cf08d63-ebf9-48a2-9bf1-acdf2bf5d4e6 SEQUENCE:4 CREATED;VALUE=DATE-TIME:20211018T044108Z DESCRIPTION:Every minor-closed class of matroids of bounded branch-width c an be characterized by a minimal list of excluded minors\, but unlike grap hs\, this list could be infinite in general. However\, for each fixed fini te field 𝔽\, the list contains only finitely many 𝔽-representable ma troids\, due to the well-quasi-ordering of 𝔽-representable matroids of bounded branch-width under taking matroid minors [J. F. Geelen\, A. M. H. Gerards\, and G. Whittle (2002)]. But this proof is non-constructive and d oes not provide any algorithm for computing these 𝔽-representable exclu ded minors in general. \nWe consider the class of matroids of path-width a t most $k$ for fixed $k$. We prove that for a finite field 𝔽\, every 𝔽-representable excluded minor for the class of matroids of path-width at most~k has at most $2^{|𝔽|^{O(k^2)}}$ elements. We can therefore com pute\, for any integer k and a fixed finite field 𝔽\, the set of 𝔽-r epresentable excluded minors for the class of matroids of path-width $k$\, and this gives as a corollary a polynomial-time algorithm for checking wh ether the path-width of an 𝔽-represented matroid is at most $k$. We als o prove that every excluded pivot-minor for the class of graphs having lin ear rank-width at most $k$ has at most $2^{2^{O(k^2)}}$ vertices\, which also results in a similar algorithmic consequence for linear rank-width of graphs.\n\nThis is joint work with Mamadou M. Kánte\, Eun Jung Kim\, and O-joung Kwon. LAST-MODIFIED;VALUE=DATE-TIME:20211103T090103Z LOCATION:BAT4 l Séminaire LIRMM - RDC Entrée\, https://bbb.lirmm.fr/b/di m-ajj-ddd URL:https://info-web.lirmm.fr/collorg/3cf08d63-ebf9-48a2-9bf1-acdf2bf5d4e6 END:VEVENT BEGIN:VEVENT SUMMARY:Alexandros Singh\, «Asymptotic Distribution of Parameters in Triv alent Maps and Linear Lambda Terms» DTSTART;VALUE=DATE-TIME:20211028T080000Z DTEND;VALUE=DATE-TIME:20211028T090000Z DTSTAMP;VALUE=DATE-TIME:20211018T133947Z UID:a4ce6d39-5971-472f-94f4-c081c299cfd9 SEQUENCE:2 CREATED;VALUE=DATE-TIME:20211018T133947Z DESCRIPTION:Structural properties of large random maps and lambda-terms ma y be gleaned by studying the limit distributions of various parameters of interest. In our work we focus on restricted classes of maps and their cou nterparts in the lambda-calculus\, building on recent bijective connection s between these two domains. In such cases\, parameters in maps naturally correspond to parameters in lambda-terms and vice versa. By an interplay b etween lambda-terms and maps\, we obtain various combinatorial specificati ons which allow us to access the distributions of pairs of related paramet ers such as: the number of bridges in rooted trivalent maps and of subterm s in closed linear lambda-terms\, the number of vertices of degree 1 in (1 \,3)-valent maps and of free variables in open linear lambda-terms etc. To analyse asymptotically these distributions\, we introduce appropriate too ls: a moment-pumping schema for differential equations and a composition s chema inspired by Bender's theorem. \n\n\nJoint work with Olivier Bodini a nd Noam Zeilberger LAST-MODIFIED;VALUE=DATE-TIME:20211027T080103Z LOCATION:BAT4 l Séminaire LIRMM - RDC Entrée & https://bbb.lirmm.fr/b/di m-ajj-ddd URL:https://info-web.lirmm.fr/collorg/a4ce6d39-5971-472f-94f4-c081c299cfd9 END:VEVENT BEGIN:VEVENT SUMMARY:Alexandre Vigny\, «Separator logic\, expressive power and algorit hmic applications» DTSTART;VALUE=DATE-TIME:20211125T090000Z DTEND;VALUE=DATE-TIME:20211125T100000Z DTSTAMP;VALUE=DATE-TIME:20211019T113649Z UID:ef436bae-498f-43e6-84fa-4df2ac4854bb SEQUENCE:6 CREATED;VALUE=DATE-TIME:20211019T113649Z DESCRIPTION:First-order logic (FO) can express many algorithmic problems o n graphs\, but fails to express whether two vertices are connected. We def ine a new logic (separator logic) by enriching FO with connectivity predic ates ${\\sf conn}_k(x\, y\, z_1\, . . . \, z_k)$ that hold true in a graph if there exists a path between x and y after deletion of $z_1\, . . . \, z_k$.\n\nJoint work with Michał Pilipczuk\, Nicole Schirrmacher\, Sebasti an Siebertz\, and Szymon Toruńczyk LAST-MODIFIED;VALUE=DATE-TIME:20211124T090103Z LOCATION:BAT4 l Séminaire LIRMM - RDC Entrée & https://bbb.lirmm.fr/b/di m-ajj-ddd URL:https://info-web.lirmm.fr/collorg/ef436bae-498f-43e6-84fa-4df2ac4854bb END:VEVENT BEGIN:VEVENT SUMMARY:Christophe Paul\, «Arrow’s theorem and impossibility theorems i n computational social choice» DTSTART;VALUE=DATE-TIME:20210506T080000Z DTEND;VALUE=DATE-TIME:20210506T090000Z DTSTAMP;VALUE=DATE-TIME:20210324T120823Z UID:b3c582ea-1106-4a14-aa38-da7a2dfc9edd SEQUENCE:1 CREATED;VALUE=DATE-TIME:20210324T120823Z DESCRIPTION:Est-il possible de proposer un système de vote qui soit à la fois démocratique et non manipulable ?\nKenneth Arrow a reçu en 1972 le prix Nobel d’économie pour sa réponse négative\, publiée en 1951\, à cette question.\n\nPlus formellement\, Arrow montre que si un vote d’ au moins deux électeurs porte sur au moins 3 options que chaque électeur doit \nordonner totalement\, alors il n’existe pas de fonction de vote qui ordonner totalement les options et satisfait simultanément \nles prop riétés suivantes :\n1- unanimité : si tous les électeurs préfèrent u ne option à une autre\, le vote doit refléter cette unanimité.\n2- non- dictature : la fonction de vote ne retourne pas le vote d’un des électe urs (dictateur).\n3- indépendance des solutions : le classement relatif e ntre deux options par la fonction de vote ne dépend \nque des classements entre ces deux options pour chacun des électeurs.\n\nLa preuve de ce ré sultat a fait l’objet de simplifications successives pour devenir relati vement simple et élégante. Nous\nprésenterons une preuve récente. En f onction du temps disponible\, nous discuterons aussi de variantes de ce r ésultat. LAST-MODIFIED;VALUE=DATE-TIME:20210505T080103Z LOCATION:https://bbb.lirmm.fr/b/dim-ajj-ddd URL:https://info-web.lirmm.fr/collorg/b3c582ea-1106-4a14-aa38-da7a2dfc9edd END:VEVENT BEGIN:VEVENT SUMMARY:Maximilian Gorsky\, «k-Outerplanarity and Poset Dimension» DTSTART;VALUE=DATE-TIME:20210520T080000Z DTEND;VALUE=DATE-TIME:20210520T090000Z DTSTAMP;VALUE=DATE-TIME:20210505T150921Z UID:718c862f-490b-4afe-8b09-3a90733abeae SEQUENCE:2 CREATED;VALUE=DATE-TIME:20210505T150921Z DESCRIPTION:Poset dimension is an important measure of structural complexi ty for posets and studying the cover graph of a poset has proven particula rly useful when working with this parameter. Bounds on the dimension have for example been established by excluding particular (topological) minors from the cover graph\, or by only considering cover graphs with treewidth at most two. In fact\, if the cover graph is planar\, a host of other impo rtant structural parameters for posets bound their dimension\, even if thi s is not the case in general. Along these lines\, Felsner et al. in 2014 p roved that posets with outerplanar cover graphs have dimension at most 4. Motivated by this result\, we give a cubic bound for the dimension of pose ts with k-outerplanar cover graphs. As a consequence\, we also improve the bound on the dimension of planar posets with height h from $O(h^6)$ to $O (h^3)$.\nThis is joint work with Michał Seweryn. LAST-MODIFIED;VALUE=DATE-TIME:20210519T080102Z LOCATION:https://bbb.lirmm.fr/b/dim-ajj-ddd URL:https://info-web.lirmm.fr/collorg/718c862f-490b-4afe-8b09-3a90733abeae END:VEVENT BEGIN:VEVENT SUMMARY:Bertrand Marchand\, «Graph width parameters in RNA bioinformatics » DTSTART;VALUE=DATE-TIME:20220922T080000Z DTEND;VALUE=DATE-TIME:20220922T090000Z DTSTAMP;VALUE=DATE-TIME:20220623T085735Z UID:4a34e2da-3101-4991-830a-d88b77fda8e3 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20220623T085735Z DESCRIPTION:An RNA consists of a chain of molecular blocks called nucleoti des (A\, U\, G\, C)\, resulting \nfrom a transcription of a portion of a D NA strand. Although they are traditionally \nthought of as mere intermedia tes in the synthesis of proteins\, a subset of them\, \ndubbed functional RNAs\, perform as such a wide variety of biological functions. \n \nTheir functions are largely determined by their 3D structures\, i.e. the way nuc leotides \nare paired up in complex folding conformations. Understanding t he connection between \nthe composition of a given sequence and its prefer red folding conformations is therefore \nkey to understanding\, or acting upon\, many biological mechanisms. \n \nRNA bioinformatics is then tasked with tackling several computational problems that naturally \narise from t rying to understand this connection. The most natural one is folding: give n \nan RNA sequence\, try to predict the structure(s) it will preferably a dopt. \nBut one could also wonder about structure reconfiguration (how eas y it is for \nan RNA molecule to go from a folded structure to another ?) or structure-sequence \nalignment (how compatible are a given fold and a g iven sequence ?). \nAll these problems are computationally hard\, \nespec ially when going towards realistic biological models. \n \nThis talk will focus on selected instances of such landmark problems\, and on \ncurrent attempts to tackle them with exact parameterized algorithmics. A particul ar \nfocus will be given to graph algorithms\, and graph width parameters. Examples \nof graph problems emerging from this angle include minimum edg e deletion towards \na target treewidth value [1]\, or the computation of directed pathwidth for a particular \ngeometric subset of directed graphs [2]. \n \nReferences: \n[1] B. Marchand\, Y. Ponty\, L. Bulteau. Tree Diet : Reducing the Treewidth to Unlock \nFPT Algorithms in RNA Bioinformatics. Algorithms for Molecular Biology 2022. \n \n[2] L. Bulteau\, B. Marchand\ , Y. Ponty. A new parameterization for independent set \nreconfiguration a nd applications to RNA kinetics. IPEC 2021. LAST-MODIFIED;VALUE=DATE-TIME:20220921T080102Z LOCATION:https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/4a34e2da-3101-4991-830a-d88b77fda8e3 END:VEVENT BEGIN:VEVENT SUMMARY:Euiwoong Lee\, «The Karger-Stein Algorithm is Optimal for $k$-cut » DTSTART;VALUE=DATE-TIME:20210610T080000Z DTEND;VALUE=DATE-TIME:20210610T080000Z DTSTAMP;VALUE=DATE-TIME:20210426T204532Z UID:a867ca20-a0a0-4107-903a-ae1263187d78 SEQUENCE:0 CREATED;VALUE=DATE-TIME:20210426T204532Z DESCRIPTION:In the $k$-cut problem\, we are given an edge-weighted graph a nd want to find the least-weight set of edges whose deletion breaks the gr aph into $k$ connected components. Algorithms due to Karger-Stein and Thor up showed how to find such a minimum $k$-cut in time approximately $O(n^{2 k-2})$. The best lower bounds come from conjectures about the solvability of the $k$-clique problem and a reduction from $k$-clique to $k$-cut\, and show that solving $k$-cut is likely to require time $\\Omega(n^k)$. Our recent results have given special-purpose algorithms that solve the proble m in time $n^{1.98k + O(1)}$\, and ones that have better performance for s pecial classes of graphs (e.g.\, for small integer weights).\nIn this work \, we resolve the problem for general graphs\, by showing that for any fix ed $k \\geq 2$\, the Karger-Stein algorithm outputs any fixed minimum $k$- cut with probability at least $\\widehat{O}(n^{-k})$\, where $\\widehat{O} (\\cdot)$ hides a $2^{O(\\ln \\ln n)^2}$ factor. This also gives an extrem al bound of $\\widehat{O}(n^k)$ on the number of minimum $k$-cuts in an $n $-vertex graph and an algorithm to compute a minimum $k$-cut in similar ru ntime. Both are tight up to $\\widehat{O}(1)$ factors. The first main ingr edient in our result is a fine-grained analysis of how the graph shrinks-- -and how the average degree evolves---under the Karger-Stein process. The second ingredient is an extremal result bounding the number of cuts of siz e at most $(2-\\delta) OPT/k$\, using the Sunflower lemma. LAST-MODIFIED;VALUE=DATE-TIME:20210609T080102Z LOCATION:Téléseminaire: https://bbb.lirmm.fr/b/dim-ajj-ddd URL:https://info-web.lirmm.fr/collorg/a867ca20-a0a0-4107-903a-ae1263187d78 END:VEVENT BEGIN:VEVENT SUMMARY:Julien Baste\, «Diversity of Solutions: An Exploration Through th e Lens of Fixed-Parameter Tractability Theory» DTSTART;VALUE=DATE-TIME:20210603T080000Z DTEND;VALUE=DATE-TIME:20210603T090000Z DTSTAMP;VALUE=DATE-TIME:20210429T082905Z UID:16704d96-8ec3-4877-bf38-1063c18f440e SEQUENCE:0 CREATED;VALUE=DATE-TIME:20210429T082905Z DESCRIPTION:When modeling an application of practical relevance as an inst ance of a combinatorial problem X\, we are often interested not merely in finding one optimal solution for that instance\, but in finding a sufficie ntly diverse collection of good solutions. In this work we initiate a syst ematic study of diversity from the point of view of fixed-parameter tracta bility theory. First\, we consider an intuitive notion of diversity of a c ollection of solutions which suits a large variety of combinatorial proble ms of practical interest. We then present an algorithmic framework which - -automatically-- converts a tree-decomposition-based dynamic programming a lgorithm for a given combinatorial problem X into a dynamic programming al gorithm for the diverse version of X. Surprisingly\, our algorithm has a p olynomial dependence on the diversity parameter. \n\n\nJoint work with: Mi chael R. Fellows\, Lars Jaffke\, Tomáš Masařík\, Mateus de Oliveira Ol iveira\, Geevarghese Philip\, Frances A. Rosamond LAST-MODIFIED;VALUE=DATE-TIME:20210602T080103Z LOCATION:Téléseminaire: https://bbb.lirmm.fr/b/dim-ajj-ddd URL:https://info-web.lirmm.fr/collorg/16704d96-8ec3-4877-bf38-1063c18f440e END:VEVENT BEGIN:VEVENT SUMMARY:Clément Maria\, «Parameterized complexity in low dimensional top ology» DTSTART;VALUE=DATE-TIME:20230511T080000Z DTEND;VALUE=DATE-TIME:20230511T090000Z DTSTAMP;VALUE=DATE-TIME:20230420T105829Z UID:0ebc4a5d-62dd-40ed-8513-739cb18467cc SEQUENCE:1 CREATED;VALUE=DATE-TIME:20230420T105829Z DESCRIPTION:Parameterized complexity is a theory allowing a finer analysis of the complexity of algorithms\, which was originally applied to graph p roblems. In this talk\, I will survey recent results on the use of paramet ers for algorithmic and combinatorial topology\, with a focus on knots and 3-manifolds. I will try to motivate and highlight the particular flavor o f parameterized complexity when applied to the computation of quantum inva riants. I will also illustrate some of the techniques to connect combinato rial and topological parameters\, and design algorithms\, at the interface of topology\, classical and quantum computational complexity\, and combin atorics. LAST-MODIFIED;VALUE=DATE-TIME:20230510T080103Z LOCATION:E.3.23 Bâtiment 4 LIRMM\, https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/0ebc4a5d-62dd-40ed-8513-739cb18467cc END:VEVENT BEGIN:VEVENT SUMMARY:William Lochet\, «Disjoint paths on dense graphs» DTSTART;VALUE=DATE-TIME:20220106T090000Z DTEND;VALUE=DATE-TIME:20220106T100000Z DTSTAMP;VALUE=DATE-TIME:20211202T094756Z UID:464e3eef-ab47-4e19-8ce4-e1de246d7f29 SEQUENCE:4 CREATED;VALUE=DATE-TIME:20211202T094756Z DESCRIPTION:In this talk we will see the proof that the $k$-edge disjoint paths problem can be solved in polynomial time on graphs with minimum degr ee $αn$ provided $k$ is small enough (but still linear in $n$). In partic ular this implies a linear kernel on the class of graphs with linear minim um degree\, which is not possible on general graphs.\n\n\n Joint work with Lokshtanov\, Saurabh and Zehavi LAST-MODIFIED;VALUE=DATE-TIME:20220105T090103Z LOCATION:https://bbb.lirmm.fr/b/dim-ajj-ddd URL:https://info-web.lirmm.fr/collorg/464e3eef-ab47-4e19-8ce4-e1de246d7f29 END:VEVENT BEGIN:VEVENT SUMMARY:Evangelos Protopapas\, «Tree-layout based graph classes: the case of proper chordal graphs» DTSTART;VALUE=DATE-TIME:20221027T080000Z DTEND;VALUE=DATE-TIME:20221027T090000Z DTSTAMP;VALUE=DATE-TIME:20221007T201344Z UID:ee16d745-c0c7-4a8a-b0ac-6eb1a76143c7 SEQUENCE:5 CREATED;VALUE=DATE-TIME:20221007T201344Z DESCRIPTION:Many standard graph classes are known to be characterized by m eans of layouts (a permutation of its vertices) excluding some patterns. I mportant such graph classes are proper interval graphs\, interval graphs\, chordal graphs but also permutation graphs\, (co-)comparability graphs an d so on. For example\, a graph $G=(V\,E)$ is an interval graph if and only if $G$ has a layout $\\mathbf{L}$ such that for every triple of vertices such that $x\\prec_{\\mathbf{L}} y\\prec_{\\mathbf{L}} z$\, if $xz\\in E$\ , then $xy\\in E$. We call such a layout an //interval layout//. Proper in terval graphs are characterized by excluding //indifference triples//\, d efined as triples $x\\prec_{\\mathbf{L}} y\\prec_{\\mathbf{L}} z$ such tha t if $xz\\in E$\, then $xy\\in E$ and $yz\\in E$. In this talk\, we inve stigate the concept of //tree-layouts//. A tree-layout $\\mathbf{T}$ of a graph $G=(V\,E)$ is a rooted tree $(T\,r)$ equipped with a one-to-one mapp ing between $V$ and the node of $T$ such that for every edge $xy\\in E$\, either $x$ is an ancestor of $y$\, denoted $x\\prec_{\\mathbf{T}} y$\, or $y$ is an ancestor of $x$. Excluding a pattern in a tree-layout is define d similarly as excluding a pattern in a layout\, but now using the ancesto r relation. It can be easily observed that chordal graphs are characterize d by the existence of a tree-layout that excludes the interval pattern dis cussed above. As a proof of concept\, we show that excluding indifference triples in tree-layouts yields a natural graph class of //proper chordal g raphs//. We will position proper chordal graphs with respect to other know n graph classes and explore its structural and algorithmic aspects.\n\nJoi nt work with Christophe Paul LAST-MODIFIED;VALUE=DATE-TIME:20221026T080102Z LOCATION:E.3.23 Bâtiment 4 LIRMM\, https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/ee16d745-c0c7-4a8a-b0ac-6eb1a76143c7 END:VEVENT BEGIN:VEVENT SUMMARY:Petra Wolf\, «Kernelizing Temporal Exploration Problems» DTSTART;VALUE=DATE-TIME:20240229T090000Z DTEND;VALUE=DATE-TIME:20240229T090000Z DTSTAMP;VALUE=DATE-TIME:20240122T170552Z UID:dbf0bff1-7c87-4811-bb14-f4547d50f8c3 SEQUENCE:5 CREATED;VALUE=DATE-TIME:20240122T170552Z DESCRIPTION:We study the kernelization of exploration problems on temporal graphs. A temporal graph consists of a finite sequence of snapshot graphs 𝒢 = (G₁\, G₂\, … \, G_L) that share a common vertex set but migh t have different edge sets. The non-strict temporal exploration problem (N S-TEXP for short) introduced by Erlebach and Spooner\, asks if a single ag ent can visit all vertices of a given temporal graph where the edges trave rsed by the agent are present in non-strict monotonous time steps\, i.e.\, the agent can move along the edges of a snapshot graph with infinite spee d. The exploration must at the latest be completed in the last snapshot gr aph. The optimization variant of this problem is the k-arb NS-TEXP problem \, where the agent’s task is to visit at least k vertices of the tempora l graph. We show that under standard computational complexity assumptions\ , neither of the problems NS-TEXP nor k-arb NS-TEXP allow for polynomial k ernels in the standard parameters: number of vertices n\, lifetime L\, num ber of vertices to visit k\, and maximal number of connected components pe r time step γ\; as well as in the combined parameters L+k\, L + γ\, and k+γ. On the way to establishing these lower bounds\, we answer a couple o f questions left open by Erlebach and Spooner. We also initiate the study of structural kernelization by identifying a new parameter of a temporal g raph p(𝒢) = ∑_{i=1}^L (|E(G_i)|) - |V(G)| + 1. Informally\, this para meter measures how dynamic the temporal graph is. Our main algorithmic res ult is the construction of a polynomial (in p(𝒢)) kernel for the more g eneral Weighted k-arb NS-TEXP problem\, where weights are assigned to the vertices and the task is to find a temporal walk of weight at least k.\n\n This talk is based on joined work together with Emmanuel Arrighi\, Fedor V. Fomin\, and Petr A. Golovach LAST-MODIFIED;VALUE=DATE-TIME:20240228T090103Z LOCATION:E.3.23 Bâtiment 4 LIRMM URL:https://info-web.lirmm.fr/collorg/dbf0bff1-7c87-4811-bb14-f4547d50f8c3 END:VEVENT BEGIN:VEVENT SUMMARY:Hoang LA\, «The potential method in graphs with a bounded maximum average degree» DTSTART;VALUE=DATE-TIME:20220310T090000Z DTEND;VALUE=DATE-TIME:20220317T100000Z DTSTAMP;VALUE=DATE-TIME:20211127T095845Z UID:73d2a73d-0d70-4048-88f8-142214775e09 SEQUENCE:7 CREATED;VALUE=DATE-TIME:20211127T095845Z DESCRIPTION:Theorems on graphs with bounded maximum average degree (mad) o ften employ the discharging method since it transforms the general bounded ratio between edges and vertices in the graph into local counting argumen ts and structures that are easier to study. Most of the time\, the bounded mad only serves as a counting tool for the discharging procedure. However \, improvements in this method often consists in finding new reducible con figurations (configurations that cannot appear in a minimal counter-exampl e). The potential method fits the bill perfectly as it introduces a functi on that quantifies exactly the mad surrounding a local structure. This add ition allows for a better manipulation of the mad in the reduction of new configurations. This talk will introduce the concept of basic operations w ith the potential function in the class of graphs with bounded mad. LAST-MODIFIED;VALUE=DATE-TIME:20220310T090340Z LOCATION:https://umontpellier-fr.zoom.us/j/95292502565 URL:https://info-web.lirmm.fr/collorg/73d2a73d-0d70-4048-88f8-142214775e09 END:VEVENT BEGIN:VEVENT SUMMARY:Sebastian Wiederrecht\, «Killing a Vortex» DTSTART;VALUE=DATE-TIME:20220127T090000Z DTEND;VALUE=DATE-TIME:20220127T100000Z DTSTAMP;VALUE=DATE-TIME:20211206T134349Z UID:3efb23db-350c-4f2f-a206-55e16210db52 SEQUENCE:23 CREATED;VALUE=DATE-TIME:20211206T134349Z DESCRIPTION:The Structural Theorem of the Graph Minors series of Robertso n and Seymour asserts that\, for every $t\\in\\Bbb{N}$\, there exists som e constant $c_{t}$ such that every graph minor-excluding $K_{t}$ admits a tree decomposition\, of adhesion at most $c_{t}$\, whose torsos can be transformed\, by the removal of at most $c_{t}$ vertices\, to graphs that can be seen as the union of some graph that is embeddable to some surface of genus at most $c_{t}$ and "at most $c_{t}$ vortices of depth $c_{t}$'' . Our main combinatorial result is a "vortex-free'' refinement of the abov e structural theorem as follows: we identify a universal graph called sha llow vortex grid $H_{t}$ and we prove that if\, in the above structural theorem\, we replace $K_{t}$ by $H_{t}$\, then the resulting decomposit ions become "vortex-free''. Up to now\, the most general classes of graph s admitting such a result were either bounded genus graphs or the so calle d single-crossing minor-free graphs. Our result is tight in the sense that \, whenever we minor-exclude a graph that is not a minor of some $H_{t}$\ , the appearance of vortices is unavoidable. Using the above decompositio n theorem\, we prove that\, on $H_{t}$-minor-free graphs\, the generating function of perfect matchings can be computed in polynomial time. This alg orithm yields\, on $H_{t}$-minor-free graphs\, polynomial algorithms for computational problems such as the dimer problem\, the exact matching problem\, and the computation of the permanent. Our results\, combined wi th known complexity results\, imply a complete characterization of minor-c losed graphs classes where the number of perfect matchings is polynomially computable: They are exactly those graph classes that do not contain ever y $H_{t}$ as a minor. This provides a //sharp complexity dichotomy// for t he problem of counting perfect matchings in minor-closed classes.\n\n\nJoi nt work with Dimitrios M. Thilikos LAST-MODIFIED;VALUE=DATE-TIME:20230617T181331Z LOCATION:https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/3efb23db-350c-4f2f-a206-55e16210db52 END:VEVENT BEGIN:VEVENT SUMMARY:Dimitrios M. Thilikos\, «Universal Obstructions of Graph Paramete rs» DTSTART;VALUE=DATE-TIME:20230629T080000Z DTEND;VALUE=DATE-TIME:20230629T090000Z DTSTAMP;VALUE=DATE-TIME:20230617T181637Z UID:7212c541-2f5b-46b1-a436-25d6380883fa SEQUENCE:5 CREATED;VALUE=DATE-TIME:20230617T181637Z DESCRIPTION:We introduce the notion of universal obstruction of a graph pa rameter\, with respect to some quasi-ordering relation. Universal obstruct ions may serve as compact characterizations of the asymptotic behavior of graph parameters. We provide order-theoretic conditions which imply that s uch a characterization is finite. We formally present the concepts of Univ ersal Obstruction\, Class Obstruction\, and Parametric Obstruction. We als o present some algorithmic implications on the existence of fixed-paramete r algorithms.\n\nJoint work with Christophe Paul and Evangelos Protopapas LAST-MODIFIED;VALUE=DATE-TIME:20230628T080102Z LOCATION:E.3.23 Bâtiment 4 LIRMM\, https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/7212c541-2f5b-46b1-a436-25d6380883fa END:VEVENT BEGIN:VEVENT SUMMARY:Laure Morelle\, «Faster parameterized algorithms for modification problems to minor-closed classes» DTSTART;VALUE=DATE-TIME:20221013T080000Z DTEND;VALUE=DATE-TIME:20221013T090000Z DTSTAMP;VALUE=DATE-TIME:20221004T144711Z UID:6907b36c-8e65-489a-befb-8abf719eb2e5 SEQUENCE:9 CREATED;VALUE=DATE-TIME:20221004T144711Z DESCRIPTION:Let ${\\cal G}$ be a minor-closed graph class and let $G$ be a n $n$-vertex graph. We say that $G$ is a $k$-apex of ${\\cal G}$ if $G$ co ntains a set $S$ of at most $k$ vertices such that $G\\setminus S$ belongs to ${\\cal G}$. Our first result is an algorithm that decides whether $G$ is a $k$-apex of ${\\cal G}$ in time $2^{{\\sf poly}(k)}\\cdot n^2$\, whe re **poly** is a polynomial function depending on ${\\cal G}$.\n\nThis alg orithm improves the previous one\, given by Sau\, Stamoulis\, and Thilikos [ICALP 2020]\, whose running time was $2^{{\\sf poly}(k)}\\cdot n^3$.\n\n \nThe elimination distance of $G$ to ${\\cal G}$\, denoted by ${\\sf ed}_{ \\cal G}(G)$\, is the minimum number of rounds required to reduce each con nected component of $G$ to a graph in ${\\cal G}$ by removing one vertex f rom each connected component in each round. Bulian and Dawar [Algorithmica 2017] provided an FPT-algorithm\, with parameter $k$\, to decide whether ${\\sf ed}_{\\cal G}(G)\\leq k$. This algorithm is based on the computabi lity of the minor-obstructions and its dependence on $k$ is not explicit. We extend the techniques used in the first algorithm to decide whether ${ \\sf ed}_{\\cal G}(G)\\leq k$ in time $2^{2^{2^{k^{O(1)}}}}\\cdot n^2$. Th is is the first algorithm for this problem with an explicit parametric dep endence in $k$. In the special case where ${\\cal G}$ excludes some apex-g raph as a minor\, we give two alternative algorithms\, one running in time $2^{2^{O(k^2\\log k)}}\\cdot n^2$ and one running in time $2^{{\\sf poly }(k)}\\cdot n^3$. As a stepping stone for these algorithms\, we provide an algorithm that decides whether ${\\sf ed}_{\\cal G}(G)\\leq k$ in time $2 ^{{\\cal O}({\\sf tw}\\cdot k + {\\sf tw}\\log {\\sf tw})}\\cdot n$\, wher e ${\\sf tw}$ is the treewidth of $G$. This algorithm combines the dynamic programming framework of Reidl\, Rossmanith\, Villaamil\, and Sikdar [ ICALP 2014] for the particular case where ${\\cal G}$ contains only the em pty graph (i.e.\, for treedepth) with the representative-based techniques introduced by Baste\, Sau\, and Thilikos [SODA 2020]. Finally\, we provid e explicit upper bounds on the size of the graphs in the minor-obstructio n set of the class of graphs ${\\cal E}_k({\\cal G})=\\{G \\mid {\\sf ed}_ {\\cal G}(G)\\leq k\\}$.\n\nJoint work with Ignasi Sau\, Giannos Stamoulis \, and Dimitrios M. Thilikos LAST-MODIFIED;VALUE=DATE-TIME:20221013T071442Z LOCATION:E.3.23 Bâtiment 4 LIRMM\, https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/6907b36c-8e65-489a-befb-8abf719eb2e5 END:VEVENT BEGIN:VEVENT SUMMARY:Ana Silva\, «Menger-related Problems on Temporal Graphs» DTSTART;VALUE=DATE-TIME:20230921T080000Z DTEND;VALUE=DATE-TIME:20230921T090000Z DTSTAMP;VALUE=DATE-TIME:20230617T182812Z UID:5ee2043c-692f-4f8c-bea4-240933240a89 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20230617T182812Z DESCRIPTION:A temporal graph is a graph that changes in time\, meaning tha t\, at each timestamp\, only a subset of the edges is active. This structu re models all sorts of real-life situations\, from social networks to publ ic transportation\, having been used also for contact tracing during the C OVID pandemic. Despite its broad applicability\, and despite being around for more than two decades\, only recently this structure has received more attention from the community. In this talk\, we will discuss how to bring some connectivity concepts to the temporal context\, and we will learn ab out the state of the art of complexity results of the related problems. Ad ditionally\, we will see various possible adaptations of Menger’s Theore m\, only a few of which also hold on temporal graphs. \n\nThe results pres ented in this talk were obtained in collaboration with Allen Ibiapina (Uni versidade Federal do Ceará\, Brazil)\, Raul Lopes (École Normale Supéri eure de Paris\, France) and Andrea Marino (University of Florence\, Italy) . LAST-MODIFIED;VALUE=DATE-TIME:20230920T093439Z LOCATION:BAT4 l Séminaire (LIRMM - RDC Entrée) URL:https://info-web.lirmm.fr/collorg/5ee2043c-692f-4f8c-bea4-240933240a89 END:VEVENT BEGIN:VEVENT SUMMARY:Open Problem Session\, «Open Problem Session of AlGCo Team» DTSTART;VALUE=DATE-TIME:20230608T080000Z DTEND;VALUE=DATE-TIME:20230608T080000Z DTSTAMP;VALUE=DATE-TIME:20230523T182946Z UID:a61d9668-5687-4eb3-a100-19d6dc371600 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20230523T182946Z DESCRIPTION:Open problems session of AlGCo-team LAST-MODIFIED;VALUE=DATE-TIME:20230607T080102Z LOCATION:E.3.23 Bâtiment 4 LIRMM\, https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/a61d9668-5687-4eb3-a100-19d6dc371600 END:VEVENT BEGIN:VEVENT SUMMARY:Marin Bougeret\, «Kernelization for Graph Packing Problems via Ra inbow Matching» DTSTART;VALUE=DATE-TIME:20230105T090000Z DTEND;VALUE=DATE-TIME:20230105T100000Z DTSTAMP;VALUE=DATE-TIME:20221013T064720Z UID:c11e05d3-f757-4ad4-8431-56d81b9f3684 SEQUENCE:4 CREATED;VALUE=DATE-TIME:20221013T064720Z DESCRIPTION:We introduce a new kernelization tool\, called //rainbow matc hing technique//\, that is appropriate for the design of polynomial kernel s for packing problems. Our technique capitalizes on the powerful combina torial results of //[Graf\, Harris\, Haxell\, SODA 2021}]//.\nWe apply the rainbow matching technique on two (di)graph packing problems\, namely th e //Triangle-Packing in Tournament// problem (**TPT**)\, where we ask for a directed triangle packing in a tournament\, and the //Induced 2-Path- Packing// (**IPP**) where we ask for a packing of $k$ induced paths of len gth two in a graph. The existence of a sub-quadratic kernels for these pr oblems was proven for the first time in //[Fomin\, Le\, Lokshtanov\, Sau rabh\, Thomassé\, Zehavi. ACM Trans. Algorithms\, 2019]//\, where they gave a kernel of ${\\cal O}(k^{3/2})$ vertices and ${\\cal O}(k^{5/3})$ vertices respectively. In the same paper it was questioned whether these bounds can be (optimally) improved to linear ones. Motivated by this ques tion\, we apply the rainbow matching technique and prove that **TPT ** a dmits an (almost linear) kernel of $k^{1+\\frac{O(1)}{\\sqrt{\\log{k}}}}$ vertices\nand that **IPP** admits kernel of ${\\cal O}(k)$ vertices.\n\nJ oint work with Stéphane Bessy\, Dimitrios M. Thilikos\, and Sebastian Wie derrecht LAST-MODIFIED;VALUE=DATE-TIME:20230104T090103Z LOCATION:E.3.23 Bâtiment 4 LIRMM\, https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/c11e05d3-f757-4ad4-8431-56d81b9f3684 END:VEVENT BEGIN:VEVENT SUMMARY:Petru Valicov\, «CAI-partitions in oriented planar graphs» DTSTART;VALUE=DATE-TIME:20251002T080000Z DTEND;VALUE=DATE-TIME:20251002T090000Z DTSTAMP;VALUE=DATE-TIME:20250929T093037Z UID:0a065360-a4bc-404b-9223-134446afb404 SEQUENCE:0 CREATED;VALUE=DATE-TIME:20250929T093037Z DESCRIPTION:It is well-known that there exist planar graphs which cannot b e vertex-partitionned into 2 forests. However\, it is a long standing conj ecture whether Eulerian planar triangulations admit such a vertex-partitio n (Barnette 1969). The "oriented" restrictions are also open: does every E ulerian oriented planar triangulation admit a vertex-partition into 2 dire cted acyclic graphs (Barnette x Neumann-Lara) ? A CAI-partition (A\,I) of a (oriented) graph is a vertex-partition in two parts A and I\, where A in duces a connected acyclic (oriented) graph and I is an independent set. An angle to attack the above mentionned conjectures\, is to use 3-colorabili ty of Eulerian triangulations\, and try to build a CAI-partition for the subgraph induced by two out of three color classes. We show that this is n ot always possible. On the positive side\, we show that bipartite 2-vertex -connected subcubic oriented graphs admit a CAI-partition\, and (almost) n one of the restrictions can be dropped. \n\nJoint work with Stijn Cambie\, François Dross\, Kolja Knauer and Hoang La. LAST-MODIFIED;VALUE=DATE-TIME:20251001T080103Z LOCATION:salle 23 bat 4 URL:https://info-web.lirmm.fr/collorg/0a065360-a4bc-404b-9223-134446afb404 END:VEVENT BEGIN:VEVENT SUMMARY:Michel Habib\, «Graph searches\, discrete geometric convexities a nd greediness» DTSTART;VALUE=DATE-TIME:20221215T090000Z DTEND;VALUE=DATE-TIME:20221215T100000Z DTSTAMP;VALUE=DATE-TIME:20221014T061515Z UID:3930d8a7-b12a-41ba-bbbc-774ef8ddf557 SEQUENCE:2 CREATED;VALUE=DATE-TIME:20221014T061515Z DESCRIPTION:We show some of the links between properties of graph searches used to recognize hereditary classes of graphs and discrete geometric con vexities. Not only this framework unifies many scattered results but also it allows to consider many new interesting problems. Moreover we consider greediness yielded by some graph searches (such as the lexicographic ones) and show how to use this greediness to solve optimization problems.\n\nJo int work with Feodor Dragan (Kent\, USA) and Lalla Mouatadib (Toronto\, C anada) LAST-MODIFIED;VALUE=DATE-TIME:20221214T090102Z LOCATION:E.3.23 Bâtiment 4 LIRMM\, https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/3930d8a7-b12a-41ba-bbbc-774ef8ddf557 END:VEVENT BEGIN:VEVENT SUMMARY:Yann Marin\, «Introduction to convexity in oriented matroid for o riented graph» DTSTART;VALUE=DATE-TIME:20221110T093000Z DTEND;VALUE=DATE-TIME:20221110T100000Z DTSTAMP;VALUE=DATE-TIME:20221020T053647Z UID:4750e9fd-5cb5-4b58-a7ea-11cc254bb3ae SEQUENCE:1 CREATED;VALUE=DATE-TIME:20221020T053647Z DESCRIPTION:We introduce the notion of convexity in oriented matroid and f ocus on how it applies to oriented graph. We will introduce some core defi nition of usual convex geometry such as face\, convex hull etc... then we may look at what mean some important convexity theorem in an oriented grap h and expose some problem we are interested in. For this part we will alte rnate between digraph properties and oriented matroid properties\, it will illustrate the differences and the similitudes of the two structures. LAST-MODIFIED;VALUE=DATE-TIME:20221109T093103Z LOCATION:E.3.23 Bâtiment 4 LIRMM\, https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/4750e9fd-5cb5-4b58-a7ea-11cc254bb3ae END:VEVENT BEGIN:VEVENT SUMMARY:Nicole Schirrmacher\, «Separator logic and disjoint-paths logic o n topological-minor-free graphs» DTSTART;VALUE=DATE-TIME:20221124T090000Z DTEND;VALUE=DATE-TIME:20221124T100000Z DTSTAMP;VALUE=DATE-TIME:20221020T054950Z UID:dc5a703f-9a54-4cbc-b5d3-8160d5470c87 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20221020T054950Z DESCRIPTION:The well-known theorem of Courcelle states that every problem expressible in monadic second-order logic is fixed-parameter tractable on classes of graphs with bounded treewidth. A more recent result of Grohe\, Kreutzer and Siebertz shows that every problem expressible in first-order logic is fixed-parameter tractable on classes of nowhere dense graphs. We try to close the gap between first-order logic and monadic second-order lo gic by new logics such as separator logic and disjoint-paths logic. We sho w that every problem expressible in separator logic or disjoint-paths logi c is fixed-parameter tractable on classes of graphs that exclude a fixed g raph as a topological minor.\n\nThis talk is based on joint work with Mich ał Pilipczuk\, Sebastian Siebertz\, Giannos Stamoulis\, Dimitrios Thiliko s\, Szymon Toruńczyk and Alexandre Vigny LAST-MODIFIED;VALUE=DATE-TIME:20221123T090103Z LOCATION:E.3.23 Bâtiment 4 LIRMM\, https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/dc5a703f-9a54-4cbc-b5d3-8160d5470c87 END:VEVENT BEGIN:VEVENT SUMMARY:Yann Marin\, «On transversal matroid and the Pascal Matroid» DTSTART;VALUE=DATE-TIME:20221110T090000Z DTEND;VALUE=DATE-TIME:20221110T093000Z DTSTAMP;VALUE=DATE-TIME:20221010T181001Z UID:713187b3-3d18-4457-9cab-6c668f3a956a SEQUENCE:4 CREATED;VALUE=DATE-TIME:20221010T181001Z DESCRIPTION:We introduce some important notion of (non oriented) matroid o n an interesting example that appear on the tiling of the (finite) triangu lar lattice by rhombus. Let T(n) be an equilateral triangle of size n made by n(n+1)/2 black triangles and n(n-1)/2 white triangles. We will show ho w all the set B of n black triangles such that T(n)/B is tillable by bicol ored rhombus are related to a matroid. We will then discuss some of its im portant properties and how it is surprisingly related to a particular cell ular automata problem. The core of this part is the relation between match ing in bipartite graph and the bases of a transversal matroid. LAST-MODIFIED;VALUE=DATE-TIME:20221109T090103Z LOCATION:E.3.23 Bâtiment 4 LIRMM\, https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/713187b3-3d18-4457-9cab-6c668f3a956a END:VEVENT BEGIN:VEVENT SUMMARY:Chien-Chung Huang\, «Robust Sparsification for Matroid Intersecti on with Applications» DTSTART;VALUE=DATE-TIME:20231207T090000Z DTEND;VALUE=DATE-TIME:20231207T100000Z DTSTAMP;VALUE=DATE-TIME:20231117T145818Z UID:0509bce4-5993-444e-bf50-f2303d1cc9e5 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20231117T145818Z DESCRIPTION:Matroid intersection is a classical optimization problem where \, given two matroids over the same ground set\, the goal is to find the l argest common independent set. We show how to construct a certain ``sparsi fer'': a subset of elements\, of size $O(|S^{opt}| \\cdot 1/\\varepsilon)$ \, where $S^{opt}$ denotes the optimal solution\, that is guaranteed to co ntain a $3/2 + \\varepsilon$ approximation\, while guaranteeing certain ro bustness properties. We call such a small subset a //Density Constrained S ubset// (DCS)\, which is inspired by the //Edge-Degree Constrained Subgrap h// (EDCS) [Bernstein and Stein\, 2015]\, originally designed for the maxi mum cardinality matching problem in a graph. Our proof is constructive and hinges on a greedy decomposition of matroids\, which we call the //densit y-based decomposition//. We show that this sparsifier has certain robustne ss properties that can be used in one-way communication and random-order s treaming models. LAST-MODIFIED;VALUE=DATE-TIME:20231206T090103Z LOCATION:E.3.24 Bâtiment 4 LIRMM URL:https://info-web.lirmm.fr/collorg/0509bce4-5993-444e-bf50-f2303d1cc9e5 END:VEVENT BEGIN:VEVENT SUMMARY:Giannos Stamoulis\, «Model-Checking for First-Order Logic with Di sjoint Paths Predicates in Proper Minor-Closed Graph Classes» DTSTART;VALUE=DATE-TIME:20230309T090000Z DTEND;VALUE=DATE-TIME:20230309T100000Z DTSTAMP;VALUE=DATE-TIME:20221020T082229Z UID:1b169768-ca2b-415b-adba-07c0ee81aca8 SEQUENCE:11 CREATED;VALUE=DATE-TIME:20221020T082229Z DESCRIPTION:The //disjoint paths logic//\, FOL+DP\, is an extension of Fi rst Order Logic (FOL) with the extra atomic predicate dp$_k(x_1\,y_1\,\\ld ots\,x_k\,y_k)\,$ expressing the existence of internally vertex-disjoint p aths between $x_i$ and $y_i\,$ for $i\\in \\{1\,\\ldots\, k\\}$. This logi c can express a wide variety of problems that escape the expressibility po tential of FOL. We prove that for every minor-closed graph class\, model-c hecking for FOL+DP can be done in quadratic time. We also introduce an ext ension of FOL+DP\, namely the //scattered disjoint paths logic//\, FOL+SDP \, where we further consider the atomic predicate $s$-sdp$_k(x_1\,y_1\,\ \ldots\,x_k\,y_k)\,$ demanding that the disjoint paths are within distanc e bigger than some fixed value $s$. Using the same technique we prove tha t model-checking for FOL+SDP can be done in quadratic time on classes of graphs with bounded Euler genus.\n\nJoint work with Petr Golovach and Dimi trios M. Thilikos LAST-MODIFIED;VALUE=DATE-TIME:20230308T090102Z LOCATION:E.3.23 Bâtiment 4 LIRMM\, https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/1b169768-ca2b-415b-adba-07c0ee81aca8 END:VEVENT BEGIN:VEVENT SUMMARY:Oscar Defrain\, «Minimal dominating sets enumeration with FPT-del ay parameterized by the (degeneracy and) maximum degree» DTSTART;VALUE=DATE-TIME:20231130T090000Z DTEND;VALUE=DATE-TIME:20231130T100000Z DTSTAMP;VALUE=DATE-TIME:20231019T140747Z UID:46b38c5c-3a46-4fc7-b9c0-33232a1b6df8 SEQUENCE:4 CREATED;VALUE=DATE-TIME:20231019T140747Z DESCRIPTION:At STOC 2002\, Eiter\, Gottlob\, and Makino presented a techni que called ordered generation that yields an $n^{O(d)}$-delay algorithm li sting all minimal transversals of an n-vertex hypergraph of degeneracy $d$ . Recently at IWOCA 2019\, Conte\, Kanté\, Marino\, and Uno asked whether this XP-delay algorithm parameterized by d could be made FPT-delay parame terized by $d$ and the maximum degree Δ\, i.e.\, an algorithm with delay $f(d\,Δ)⋅n^{O(1)}$ for some computable function f. Moreover\, as a firs t step toward answering that question\, they note that the same delay is o pen for the intimately related problem of listing all minimal dominating s ets in graphs. In this paper\, we answer the latter question in the affirm ative.\n\nJoint work with Valentin Bartier and Fionn Mc Inerney LAST-MODIFIED;VALUE=DATE-TIME:20231129T090102Z LOCATION:E.3.24 Bâtiment 4 LIRMM et https://umontpellier-fr.zoom.us/j/952 92502565 URL:https://info-web.lirmm.fr/collorg/46b38c5c-3a46-4fc7-b9c0-33232a1b6df8 END:VEVENT BEGIN:VEVENT SUMMARY:Benjamin Bergougnoux\, «Tight Lower Bounds for Problems Parameter ized by Rank-width» DTSTART;VALUE=DATE-TIME:20221201T090000Z DTEND;VALUE=DATE-TIME:20221201T100000Z DTSTAMP;VALUE=DATE-TIME:20221101T120758Z UID:16759ee4-caa7-4bb8-bd99-4a669f8ea3c5 SEQUENCE:5 CREATED;VALUE=DATE-TIME:20221101T120758Z DESCRIPTION:We show that there is no $2^{o(k^2)} n^{O(1)}$ time algorithm for Independent Set on $n$-vertex graphs with rank-width $k$\, unless the Exponential Time Hypothesis (ETH) fails. Our lower bound matches the $2^{O (k^2)} n^{O(1)}$ time algorithm given by Bui-Xuan\, Telle\, and Vatshelle [Discret. Appl. Math.\, 2010] and it answers the open question of Bergougn oux and Kanté [SIAM J. Discret. Math.\, 2021]. We also show that the know n $2^{O(k^2)} n^{O(1)}$ time algorithms for Weighted Dominating Set\, Maxi mum Induced Matching and Feedback Vertex Set parameterized by rank-width $ k$ are optimal assuming ETH. Our results are the first tight ETH lower bou nds parameterized by rank-width that do not follow directly from lower bou nds for $n$-vertex graphs. LAST-MODIFIED;VALUE=DATE-TIME:20221130T090103Z LOCATION:https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/16759ee4-caa7-4bb8-bd99-4a669f8ea3c5 END:VEVENT BEGIN:VEVENT SUMMARY:Aliaume Lopez\, «Locality and the Łoś–Tarski Theorem in Finit e Model Theory» DTSTART;VALUE=DATE-TIME:20230208T090000Z DTEND;VALUE=DATE-TIME:20230208T100000Z DTSTAMP;VALUE=DATE-TIME:20231218T142640Z UID:95dfb912-4686-44e7-ac27-191175f9aa92 SEQUENCE:0 CREATED;VALUE=DATE-TIME:20231218T142640Z DESCRIPTION:Preservation theorems are classical results from Model Theory\ , stating that syntactic fragments of first-order logic (existential sente nces\, existential positive sentences\, etc) are characterised by semantic properties (sentences preserved under extensions\, preserved under inject ive homomorphisms\, etc). The status of these results in finite model theo ry (that is\, restricting the statement to classes of finite structures) i s non trivial. Indeed\, the classical proofs of these results rely on the compactness theorem of first-order logic\, which is known to fail in the f inite. Furthermore\, on restricted classes of structures\, semantic charac terisations become weaker (for instance\, it is easier to be preserved und er extensions when fewer structures belong to the class)\, and syntactic e quivalences become weaker too (more sentences are equivalent when tested o ver fewer models).\n\nUnderstanding over which classes of finite structure s preservation theorems relativise involves tools from finite model theory (locality of first order logic)\, requires combinatorial results (mainly about the spatial distribution of types of neighbourhoods in finite struct ures)\, and even features some usage of monadic second order logic. While preservation theorems are interesting in themselves (because they have con nections with well-quasi-orders\, and characterise termination of some dat abase algorithms such as the Chase)\, their study also provides deep insig ht into which classes of structures are “well-behaved” with respect to first-order logic.\n\nIn this talk\, we will focus on one particular pres ervation theorem\, the Łoś–Tarski Theorem\, and prove that this theore m relativises to a class 𝒞 of finite structures if and only if it relat ivises locally to the class 𝒞\, which will illustrate the aforementione d techniques.\n\nThis talk is based on the results published at LICS 2022 in the paper “When Locality Meets Preservation”. LAST-MODIFIED;VALUE=DATE-TIME:20231218T142640Z LOCATION:E.3.24 Bâtiment 4 LIRMM et https://umontpellier-fr.zoom.us/j/952 92502565 URL:https://info-web.lirmm.fr/collorg/95dfb912-4686-44e7-ac27-191175f9aa92 END:VEVENT BEGIN:VEVENT SUMMARY:Christophe Paul\, «Linear time modular decomposition algorithm» DTSTART;VALUE=DATE-TIME:20231019T080000Z DTEND;VALUE=DATE-TIME:20231019T090000Z DTSTAMP;VALUE=DATE-TIME:20230608T103338Z UID:26d0a0a7-e10c-4b9c-908b-626b259d4681 SEQUENCE:5 CREATED;VALUE=DATE-TIME:20230608T103338Z DESCRIPTION:There is a long history of modular decomposition algorithms st arting in the 70’s with a $O(n^4)$ algorithm. The first linear time algo rithms appeared in 1994 (by Cournier\, Habib and by McConnell\, Spinrad). Since them simplified (almost) linear time algorithms have been proposed. I will describe one based on LexBFS and a tree-partition refinement techni que. The complexity analysis requires a carefully amortized analysis that we will discuss.\n\n\nThis is a joint work with D. Corneil\, M. Habib and M. Tedder that was originally presented at ICALP’08\, but which full ver sion is still lacking. LAST-MODIFIED;VALUE=DATE-TIME:20231018T080103Z LOCATION:salle : E.3.24 Bâtiment 4 LIRMM URL:https://info-web.lirmm.fr/collorg/26d0a0a7-e10c-4b9c-908b-626b259d4681 END:VEVENT BEGIN:VEVENT SUMMARY:Júlio Araújo\, «Semi-proper orientations of dense graphs» DTSTART;VALUE=DATE-TIME:20240111T090000Z DTEND;VALUE=DATE-TIME:20240118T100000Z DTSTAMP;VALUE=DATE-TIME:20231115T125809Z UID:1e0c977f-e6f3-465c-a271-0810f1c37ace SEQUENCE:11 CREATED;VALUE=DATE-TIME:20231115T125809Z DESCRIPTION:An //orientation// $D$ of a graph $G$ is a digraph obtained fr om $G$ by replacing each edge by exactly one of the two possible arcs with the same ends. An orientation $D$ of a graph $G$ is a //$k$-orientation// if the in-degree of each vertex in $D$ is at most $k$. An orientation $D $ of $G$ is //proper// if any two adjacent vertices have different in-degr ees in $D$. The //proper orientation number// of a graph $G$\, denoted by $po(G)$\, is the minimum $k$ such that $G$ has a proper $k$-orientation.\n \nA //weighted orientation// of a graph $G$ is a pair $(D\,w)$\, where $D$ is an orientation of $G$ and $w$ is an arc-weighting $A(D) \\to \\mathbb {N}\\setminus\\{0\\}$. A //semi-proper orientation// of $G$ is a weighted orientation $(D\,w)$ of $G$ such that for every two adjacent vertices $u$ and $v$ in $G$\, we have that $S_{(D\,w)}(v) \\neq S_{(D\,w)}(u) $\, where \n$S_{(D\,w)}(v)$ is the sum of the weights of the arcs in $(D\,w)$ with h ead $v$. For a positive integer $k$\, a //semi-proper $k$-orientation// $( D\,w)$ of a graph $G$ is a semi-proper orientation of $G$ such that $\\max _{v\\in V(G)} S_{(D\,w)}(v) ≤ k$. The //semi-proper orientation number// of a graph $G$\, denoted by $spo(G)$\, is the least $k$ such that $G$ has a semi-proper $k$-orientation.\n\nIn this work\, we first prove that $spo (G) \\in \\{ω(G)-1\,ω(G)\\}$ for every split graph $G$\, and that\, give n a split graph $G$\, deciding whether $spo(G) = ω(G)-1$ is an $NP$-compl ete problem. We also show that\, for every $k$\, there exists a (chordal) graph $G$ and a split subgraph $H$ of $G$ such that $po(G) ≤ k$ and $po( H) = 2k-2$. In the sequel\, we show that\, for every $n≥ p(p+1)$\, $spo( P^{p}_n) = \\left\\lceil \\frac{3}{2}p \\right\\rceil$\, where $P^{p}_n$ i s the $p^{th}$ power of the path on $n$ vertices. We investigate further u nit interval graphs with no big clique: we show that $po(G) ≤ 3$ for any unit interval graph $G$ with $ω(G)=3$\, and present a complete character ization of unit interval graphs with $po(G)=ω(G)=3$. Then\, we show that deciding whether $spo(G)=ω(G)$ can be solved in polynomial time in the cl ass of co-bipartite graphs. Finally\, we prove that computing $spo(G)$ is FPT when parameterized by the minimum size of a vertex cover in $G$ or by the treewidth of $G$. We also prove that not only computing $spo(G)$\, but also $po(G)$\, admits a polynomial kernel when parameterized by the neigh bourhood diversity plus the value of the solution. These results imply ker nels of size $4^{{\\cal O}(k^2)}$ and ${\\cal O}(2^kk^2)$\, in chordal gra phs and split graphs\, respectively\, for the problem of deciding whether $spo(G)≤ k$ parameterized by $k$. We also present exponential kernels fo r computing both $po(G)$ and $spo(G)$ parameterized by the value of the so lution when $G$ is a cograph. On the other hand\, we show that computing $ spo(G)$ does not admit a polynomial kernel parameterized by the value of t he solution when $G$ is a chordal graph\, unless NP $\\subseteq$ coNP/poly .\n\nJoint work with F. Havet\, C. Linhares Sales\, N. Nisse and K. Suchan . LAST-MODIFIED;VALUE=DATE-TIME:20240110T090103Z LOCATION:E.3.24 Bâtiment 4 LIRMM URL:https://info-web.lirmm.fr/collorg/1e0c977f-e6f3-465c-a271-0810f1c37ace END:VEVENT BEGIN:VEVENT SUMMARY:Petr A. Golovach\, «Shortest cycles with monotone submodular cost s» DTSTART;VALUE=DATE-TIME:20230216T090000Z DTEND;VALUE=DATE-TIME:20230216T100000Z DTSTAMP;VALUE=DATE-TIME:20230205T193526Z UID:d87f2dfb-985a-4776-8b99-0a0ad5b73604 SEQUENCE:3 CREATED;VALUE=DATE-TIME:20230205T193526Z DESCRIPTION:We introduce the following submodular generalization of the Sh ortest Cycle problem. For a nonnegative monotone submodular cost function $f$ defined on the vertices (or\, equivalently\, the edges) of an undire cted graph $G$\, we seek for a cycle $C$ in $G$ of minimum cost $Opt=f(C)$ . We construct an algorithm that\, given an $n$-vertex graph $G$\, parame ter $ε > 0$\, and the function $f$ represented by an oracle\, in time $n ^{O(\\log 1/ε)}$ finds a cycle $C$ in $G$ with $f(C)\\leq (1+ε)Opt$. Thi s is in sharp contrast with the non-approximability of the closely related Monotone Submodular Shortest $(s\,t)$-Path problem\, which requires expon entially many queries to the oracle for finding an $n^{2/3-ε}$-approximat ion [Goel et al.\, FOCS 2009]. When the function $f$ is integer-valued\, our algorithm yields that a cycle of cost $Opt$ can be found in time $n^{O (\\log Opt)}$. In particular\, for $Opt=n^{O(1)}$ this gives a quasipoly nomial-time algorithm computing a cycle of minimum submodular cost.\n\nJoi nt work with: Fedor V. Fomin\, Tuukka Korhonen\, Daniel Lokshtanov\, and G iannos Stamoulis LAST-MODIFIED;VALUE=DATE-TIME:20230215T090102Z LOCATION:E.3.23 Bâtiment 4 LIRMM\, https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/d87f2dfb-985a-4776-8b99-0a0ad5b73604 END:VEVENT BEGIN:VEVENT SUMMARY:Sebastian Wiederrecht\, «Excluding Single-Crossing Matching Minor s in Bipartite Graphs» DTSTART;VALUE=DATE-TIME:20230112T090000Z DTEND;VALUE=DATE-TIME:20230112T100000Z DTSTAMP;VALUE=DATE-TIME:20221013T070950Z UID:2c56d72f-bed9-459c-80f8-d7722e4d972f SEQUENCE:4 CREATED;VALUE=DATE-TIME:20221013T070950Z DESCRIPTION:By a seminal result of Valiant\, computing the permanent of $( 0\,1)$-matrices is\, in general\, $\\#\\mathsf{P}$-hard. In 1913 Pólya a sked for which $(0\,1)$-matrices $A$ it is possible to change some signs s uch that the permanent of $A$ equals the determinant of the resulting matr ix. In 1975\, Little showed these matrices to be exactly the biadjacency m atrices of bipartite graphs excluding $K_{3\,3}$ as a \\textsl{matching mi nor}. This was turned into a polynomial time algorithm by McCuaig\, Robert son\, Seymour\, and Thomas in 1999. However\, the relation between the exc lusion of some matching minor in a bipartite graph and the tractability of the permanent extends beyond $K_{3\,3}.$ Recently it was shown that the e xclusion of any planar bipartite graph as a matching minor yields a class of bipartite graphs on which the \\textsl{permanent} of the corresponding $(0\,1)$-matrices can be computed efficiently. In this paper we unify the two results above into a single\, more general result in the style of the celebrated structure theorem for single-crossing minor-free graphs. We ide ntify a class of bipartite graphs strictly generalising planar bipartite g raphs and $K_{3\,3}$ which includes infinitely many non-Pfaffian graphs. T he exclusion of any member of this class as a matching minor yields a stru cture that allows for the efficient evaluation of the permanent. Moreover\ , we show that the evaluation of the permanent remains $\\#\\mathsf{P}$-ha rd on bipartite graphs which exclude $K_{5\,5}$ as a matching minor. This establishes a first computational lower bound for the problem of counting perfect matchings on matching minor closed classes. As another application of our structure theorem\, we obtain a strict generalisation of the algor ithm for the $k$-vertex disjoint directed paths problem on digraphs of bou nded directed treewidth.\n\n\nJoint work with Archontia C. Giannopoulou an d Dimitrios M. Thilikos LAST-MODIFIED;VALUE=DATE-TIME:20230111T090103Z LOCATION:E.3.23 Bâtiment 4 LIRMM\, https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/2c56d72f-bed9-459c-80f8-d7722e4d972f END:VEVENT BEGIN:VEVENT SUMMARY:Maximilian Gorsky\, «Packing even directed circuits quarter-integ rally» DTSTART;VALUE=DATE-TIME:20240314T090000Z DTEND;VALUE=DATE-TIME:20240314T100000Z DTSTAMP;VALUE=DATE-TIME:20231113T080248Z UID:f8fdb22f-4f07-42f9-8123-b4ed75f05ee4 SEQUENCE:7 CREATED;VALUE=DATE-TIME:20231113T080248Z DESCRIPTION:We prove the existence of a computable function f : N → N su ch that for every integer k and every digraph D either contains a collecti on C of directed cycles of even length such that no vertex of D belongs to more than four cycles in C\, or there exists a set S ⊆ V (D) of size at most f(k) such that D − S has no directed cycle of even length. Moreove r\, we provide an algorithm that finds one of the two outcomes of this sta tement in time $g(k)\\cdot n^{O(1)}$ for some computable function g : N → N.\nOur result unites two deep fields of research from the algorithmic theory for digraphs: The study of the Erdős-Pósa property of digraphs a nd the study of the Even Dicycle Problem. The latter is the decision probl em which asks if a given digraph contains an even dicycle and can be trace d back to a question of Pólya from 1913. It remained open until a polynom ial time algorithm was finally found by Robertson\, Seymour\, and Thomas ( Ann. of Math. (2) 1999) and\, independently\, McCuaig (Electron. J. Combin . 2004\; announced jointly at STOC 1997). The Even Dicycle Problem is equi valent to the recognition problem of Pfaffian bipartite graphs and has app lications even beyond discrete mathematics and theoretical computer scienc e. On the other hand\, Younger’s Conjecture (1973)\, states that dicycle s have the Erdős-Pósa property. The conjecture was proven more than two decades later by Reed\, Robertson\, Seymour\, and Thomas (Combinatorica 19 96) and opened the path for structural digraph theory as well as the algor ithmic study of the directed feedback vertex set problem. Our approach bui lds upon the techniques used to resolve both problems and combines them in to a powerful structural theorem that yields further algorithmic applicati ons for other prominent problems.\n\nJoint work with Ken-ichi Kawarabayash i\, Stephan Kreutzer\, and\nSebastian Wiederrecht LAST-MODIFIED;VALUE=DATE-TIME:20240313T090103Z LOCATION:E.3.24 Bâtiment 4 LIRMM et https://umontpellier-fr.zoom.us/j/952 92502565 URL:https://info-web.lirmm.fr/collorg/f8fdb22f-4f07-42f9-8123-b4ed75f05ee4 END:VEVENT BEGIN:VEVENT SUMMARY:Timothé Picavet \, «A parameterized approximation scheme for the 2D-Knapsack problem with wide items» DTSTART;VALUE=DATE-TIME:20231005T080000Z DTEND;VALUE=DATE-TIME:20231005T083000Z DTSTAMP;VALUE=DATE-TIME:20230925T091008Z UID:8d024431-c6f8-4ebd-99b6-f201eeb01e2f SEQUENCE:5 CREATED;VALUE=DATE-TIME:20230925T091008Z DESCRIPTION:We study a natural geometric variant of the classic Knapsack p roblem called 2D-Knapsack: we are given a set of axis-parallel rectangles and a rectangular bounding box\, and the goal is to pack as many of these rectangles inside the box without overlap. Naturally\, this problem is NP- complete. Recently\, Grandoni et al. [ESA'19] showed that it is also W[1]- hard when parameterized by the size k of the sought packing\, and they pre sented a parameterized approximation scheme (PAS) for the variant where we are allowed to rotate the rectangles by 90° before packing them into the box. Obtaining a PAS for the original 2D-Knapsack problem\, without rotat ion\, appears to be a challenging open question. We make progress towards this goal by showing a PAS under the following assumptions: 1. both the bo x and all the input rectangles have integral\, polynomially bounded sidele ngths\; 2. every input rectangle is wide -- its width is greater than its height\; and 3. the aspect ratio of the box is bounded by a constant. Our approximation scheme relies on a mix of various parameterized and approxim ation techniques\, including color coding\, rounding\, and searching for a structured near-optimum packing using dynamic programming. LAST-MODIFIED;VALUE=DATE-TIME:20231004T080103Z LOCATION:BAT4 l Séminaire (LIRMM - RDC Entrée) URL:https://info-web.lirmm.fr/collorg/8d024431-c6f8-4ebd-99b6-f201eeb01e2f END:VEVENT BEGIN:VEVENT SUMMARY:Zdeněk Dvořák\, «Approximation meta-algorithms [Déplacé/Mov ed: 15:00–16:00]» DTSTART;VALUE=DATE-TIME:20220203T140000Z DTEND;VALUE=DATE-TIME:20220203T150000Z DTSTAMP;VALUE=DATE-TIME:20211207T102747Z UID:9d652cc9-0be2-4677-abc9-333f94f8b44f SEQUENCE:9 CREATED;VALUE=DATE-TIME:20211207T102747Z DESCRIPTION:For a monotone property $π$ of subsets of vertices of a graph $G$ (being an independent set\, forming a clique in $G^2$\, ...)\, let $M AX_π(G)$ denote the size of the largest subset of $V(G)$ having this prop erty. By a fundamental result of Grohe\, Kreutzer\, and Siebertz\, if $π $ is expressible in the first-order logic\, then $MAX_π$ is fixed-paramet er tractable for graphs from any nowhere-dense class (when parameterized b y the value of the solution). We survey results on a related question: In which graph classes does $MAX_π$ admit efficient approximation algorithm s? LAST-MODIFIED;VALUE=DATE-TIME:20220202T140103Z LOCATION:https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/9d652cc9-0be2-4677-abc9-333f94f8b44f END:VEVENT BEGIN:VEVENT SUMMARY:Martin Koutecký\, «Liquid Democracy for Participatory Budgeting » DTSTART;VALUE=DATE-TIME:20220210T090000Z DTEND;VALUE=DATE-TIME:20220210T100000Z DTSTAMP;VALUE=DATE-TIME:20211123T084153Z UID:c3b829db-b701-4059-9cee-becf9322eee3 SEQUENCE:3 CREATED;VALUE=DATE-TIME:20211123T084153Z DESCRIPTION:Liquid Democracy is a form of delegative democracy which promi ses more direct participation and dynamic representation. Because it is on ly recently become realistic with the use of modern technologies\, it has been coming into the focus of research. We propose a model of liquid democ racy in the context of participatory budgeting. A common issue in the cont ext of liquid democracy is the resolution of delegation cycles -- if the v ote of A depends on B\, which depends on C\, which depends on A\, how shou ld they vote? We define several natural notions of proportionality and sho w that delegations in our model can always be satisfactorily resolved.\n\n Next\, we turn to the computational aspects of our model. By known results \, the complexity of finding a proportional delegation belongs to the clas s PPAD. Rather than showing completeness or tighter containment (in classe s such as PLS\, CLS etc.)\, we ask the practical question: is it possible to efficiently resolve delegations in "real-world" instances? We design an algorithm which seems to perform well. In the absence of real-world insta nces\, we also devise a framework to compute hard instances\; this framewo rk might be of independent interest. LAST-MODIFIED;VALUE=DATE-TIME:20220209T090103Z LOCATION:https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/c3b829db-b701-4059-9cee-becf9322eee3 END:VEVENT BEGIN:VEVENT SUMMARY:Théo Pierron \, «Extremal Independent Set Reconfiguration» DTSTART;VALUE=DATE-TIME:20230126T090000Z DTEND;VALUE=DATE-TIME:20230126T100000Z DTSTAMP;VALUE=DATE-TIME:20221118T153805Z UID:c1bfafc8-6d51-4652-b4a0-85d81f3eb6ea SEQUENCE:3 CREATED;VALUE=DATE-TIME:20221118T153805Z DESCRIPTION:The independent set reconfiguration problem asks whether one c an transform one given independent set of a graph into another\, by changi ng vertices one by one in such a way the intermediate sets remain independ ent. The goal is usually to find short transformations for graphs of a giv en class. Here\, we take an alternative\, more extremal point of view by a sking a reverse question: which graphs yield (shortest) transformations of maximum length?\n\n\nThis is joint work with Nicolas Bousquet\, Bastien D urain\, and Stéphan Thomassé. LAST-MODIFIED;VALUE=DATE-TIME:20230125T090102Z LOCATION:E.3.23 Bâtiment 4 LIRMM\, https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/c1bfafc8-6d51-4652-b4a0-85d81f3eb6ea END:VEVENT BEGIN:VEVENT SUMMARY:Guillaume Mescoff\, ««Largeur arborescente»: a forgotten old go od friend of treewidth» DTSTART;VALUE=DATE-TIME:20210617T080000Z DTEND;VALUE=DATE-TIME:20210624T090000Z DTSTAMP;VALUE=DATE-TIME:20210529T114021Z UID:ff14ff5c-e766-4e43-88fc-7069dc9ecf4d SEQUENCE:14 CREATED;VALUE=DATE-TIME:20210529T114021Z DESCRIPTION:In mixed search games\, searchers can be put\, removed from ve rtices\, or slide along edges. There are different versions of mixed searc h games depending on whether the robber is visible or invisible and lazy o r agile. We consider two graph searching parameters\, namely the minimum n umber of searchers that are required for capturing a robber that is lazy a nd invisible or\, alternatively\, agile and visible. These two graph sear ching parameter are the only search game variants whose monotonicity remai ns open up to now. In our recent work\, we show the monotonicity of these two graph searching variants by proving their equivalence to the «largeur arborescente» (la)\, a variant of treewidth defined in //[Yves Colin de Verdière: Multiplicities of Eigenvalues and Tree-Width of Graphs. Journal of Combinatorial Theory\, Series B 74(2): 121-146 (1998)]//. The largeur arborescente\, ${\\bf la}(G)$\, of a graph $G$ is defined as the minimum $k$ such that $G$ is a minor of $T \\times K_k$ for some tree $T$. The lar geur arborescente captures the tree-like structure of graphs in a smoother way than the treewidth\, is parametrically equivalent to the treewidth\, and treewidth can be reduced to it. In our work\, we contribute to the stu dy of largeur arborescente by giving eight different equivlalent character izations\, including an obstruction min-max charactereization that implies the monotonicity of the aforementioned mixed search games.\n\n\nJoint Wor k with Christophe Paul and Dimitrios M. Thilikos LAST-MODIFIED;VALUE=DATE-TIME:20221118T154012Z LOCATION:https://bbb.lirmm.fr/b/dim-ajj-ddd URL:https://info-web.lirmm.fr/collorg/ff14ff5c-e766-4e43-88fc-7069dc9ecf4d END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Gonçalves\, «On comparable box dimension» DTSTART;VALUE=DATE-TIME:20220609T080000Z DTEND;VALUE=DATE-TIME:20220609T090000Z DTSTAMP;VALUE=DATE-TIME:20220309T105813Z UID:c4298220-70a3-475a-b3c6-885f384c815b SEQUENCE:6 CREATED;VALUE=DATE-TIME:20220309T105813Z DESCRIPTION:Two boxes in $\\mathbb{R}^d$ are comparable if one of them is a subset\nof a translation of the other. The comparable box dimension of a graph\n$G$ is the minimum integer $d$ such that $G$ can be represented as a\ntouching graph of comparable axis-aligned boxes in $\\mathbb{R}^d$. We \nshow that proper minor-closed classes have bounded comparable box\ndimen sion and explore further properties of this notion. In particular we show that graphs with bounded comparable box dimension are treewidth fragile.\n \nJoint work with Z. Dvořák\, Abhiruk Lahiri\, Jane Tan\, and Torsten Ue ckerdt LAST-MODIFIED;VALUE=DATE-TIME:20220608T080102Z LOCATION:E.3.23 Bâtiment 4 LIRMM\, https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/c4298220-70a3-475a-b3c6-885f384c815b END:VEVENT BEGIN:VEVENT SUMMARY:Meike Hatzel\, «On the structure of directed graphs» DTSTART;VALUE=DATE-TIME:20220224T090000Z DTEND;VALUE=DATE-TIME:20220224T100000Z DTSTAMP;VALUE=DATE-TIME:20211102T161934Z UID:769f9515-b6cf-43e3-8f7f-5dde7a3d24c3 SEQUENCE:4 CREATED;VALUE=DATE-TIME:20211102T161934Z DESCRIPTION:In their series of over twenty papers Robertson and Seymour gi ve insight into the structure of undirected graphs. Proving a number of im pactful theorems they arrive at the structure theorem\, a description of g raphs excluding a fixed non-planar minor. A lot of work has been done in r ecent years trying to transfer such results to a directed setting. In this attempt one encounters numerous obstacles.\nIn this talk we consider thes e obstacles and possibilities to deal with them.\nWe take a look at the cu rrent state of digraph structure theory with respect to proving a structur e theorem for excluding a fixed butterfly minor. LAST-MODIFIED;VALUE=DATE-TIME:20221118T154111Z LOCATION:https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/769f9515-b6cf-43e3-8f7f-5dde7a3d24c3 END:VEVENT BEGIN:VEVENT SUMMARY:Petr Golovach\, «Longest Cycle above Erdős-Gallai Bound» DTSTART;VALUE=DATE-TIME:20220421T080000Z DTEND;VALUE=DATE-TIME:20220421T090000Z DTSTAMP;VALUE=DATE-TIME:20220308T195734Z UID:2ca5e8f1-07c2-4d92-a1ec-99dde4fe4f5c SEQUENCE:2 CREATED;VALUE=DATE-TIME:20220308T195734Z DESCRIPTION:In 1959\, Erdős and Gallai proved that every graph $G$ with a verage vertex degree $\\mathsf{ad}(G)≤ 2$ contains a cycle of length at least $\\mathsf{ad}(G)$. We provide an algorithm that for $k\\geq 0$ in ti me $2^{O(k)} n^{O(1)}$ decides whether a 2-connected n-vertex graph G cont ains a cycle of length at least $\\mathsf{ad}(G)+k$. This resolves an open problem explicitly mentioned in several papers. The main ingredients of o ur algorithm are new graph-theoretical results interesting on their own.\n \nJoint work with Fedor V. Fomin\, Danil Sagunov\, and Kirill Simonov. LAST-MODIFIED;VALUE=DATE-TIME:20220420T080103Z LOCATION:https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/2ca5e8f1-07c2-4d92-a1ec-99dde4fe4f5c END:VEVENT BEGIN:VEVENT SUMMARY:Noleen Kölher\, «Twin-Width VIII: Delineation and Win-Wins» DTSTART;VALUE=DATE-TIME:20230202T090000Z DTEND;VALUE=DATE-TIME:20230202T100000Z DTSTAMP;VALUE=DATE-TIME:20221124T125622Z UID:4d7ab6c0-a184-4a7a-be6b-623c4e39cf51 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20221124T125622Z DESCRIPTION:We introduce the notion of delineation. A graph class C is sai d delineated by twin-width (or simply\, delineated) if for every hereditar y closure D of a subclass of C\, it holds that D has bounded twin-width if and only if D is monadically dependent. An effective strengthening of del ineation for a class C implies that tractable FO model checking on C is pe rfectly understood: On hereditary closures of subclasses D of C\, FO model checking on D is fixed-parameter tractable (FPT) exactly when D has bound ed twin-width. Ordered graphs [BGOdMSTT\, STOC ’22] and permutation grap hs [BKTW\, JACM ’22] are effectively delineated\, while subcubic graphs are not. On the one hand\, we prove that interval graphs\, and even\, root ed directed path graphs are delineated. On the other hand\, we observe or show that segment graphs\, directed path graphs (with arbitrarily many roo ts)\, and visibility graphs of simple polygons are not delineated.\nIn an effort to draw the delineation frontier between interval graphs (that are delineated) and axis-parallel two-lengthed segment graphs (that are not)\, we investigate the twin-width of restricted segment intersection classes. It was known that (triangle-free) pure axis-parallel unit segment graphs have unbounded twin-width [BGKTW\, SODA ’21]. We show that Kt\,t-free se gment graphs\, and axis-parallel Ht-free unit segment graphs have bounded twin-width\, where Ht is the half-graph or ladder of height t. In contrast \, axis-parallel H4-free two-lengthed segment graphs have unbounded twin-w idth. We leave as an open question whether unit segment graphs are delinea ted.\n\nMore broadly\, we explore which structures (large bicliques\, half -graphs\, or independent sets) are responsible for making the twin-width l arge on the main classes of intersection and visibility graphs. Our new re sults\, combined with the FPT algorithm for first-order model checking on graphs given with O(1)-sequences [BKTW\, JACM ’22]\, give rise to a vari ety of algorithmic win-win arguments. They all fall in the same framework: If p is an FO definable graph parameter that effectively functionally upp erbounds twin-width on a class C\, then p(G) ⩾ k can be decided in FPT t ime f(k) · |V (G)|O(1). For instance\, we readily derive FPT algorithms f or k-Ladder on visibility graphs of 1.5D terrains\, and k-Independent Set on visibility graphs of simple polygons. This showcases that the theory of twin-width can serve outside of classes of bounded twin-width.\n\nJoint w ork with Édouard Bonnet\, Dibyayan Chakraborty\, Eun Jung Kim\, Raul Lop es and Stéphan Thomassé. LAST-MODIFIED;VALUE=DATE-TIME:20230201T090103Z LOCATION:E.3.23 Bâtiment 4 LIRMM\, https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/4d7ab6c0-a184-4a7a-be6b-623c4e39cf51 END:VEVENT BEGIN:VEVENT SUMMARY:Robert Ganian\, «Edge-Cut Width: An Algorithmically Driven Analog ue of Treewidth Based on Edge Cuts» DTSTART;VALUE=DATE-TIME:20220511T220000Z DTEND;VALUE=DATE-TIME:20220512T100000Z DTSTAMP;VALUE=DATE-TIME:20220309T104230Z UID:febdc907-0309-4409-ac19-304c27c9caa4 SEQUENCE:2 CREATED;VALUE=DATE-TIME:20220309T104230Z DESCRIPTION:Decompositional parameters such as treewidth are commonly used to\nobtain fixed-parameter algorithms for NP-hard graph problems. For\npr oblems that are W[1]-hard parameterized by treewidth\, a natural\nalternat ive would be to use a suitable analogue of treewidth that is\nbased on edg e cuts instead of vertex separators. While tree-cut width\nhas been coined as such an analogue of treewidth for edge cuts\, its\nalgorithmic applica tions have often led to disappointing results: out\nof twelve problems whe re one would hope for fixed-parameter\ntractability parameterized by an ed ge-cut based analogue to treewidth\,\neight were shown to be W[1]-hard par ameterized by tree-cut width.\n\nHere\, we will discuss an edge-cut based analogue to treewidth called\nedge-cut width. Edge-cut width is\, intuitiv ely\, based on measuring the\ndensity of cycles passing through a spanning tree of the graph. Its\nbenefits include not only a comparatively simple definition\, but\nmainly that it has interesting algorithmic properties: i t can be\ncomputed by a fixed-parameter algorithm\, and it yields fixed-pa rameter\nalgorithms for all the aforementioned problems where tree-cut wid th\nfailed to do so. LAST-MODIFIED;VALUE=DATE-TIME:20220512T074309Z LOCATION:https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/febdc907-0309-4409-ac19-304c27c9caa4 END:VEVENT BEGIN:VEVENT SUMMARY:Eric Brandwein\, «Kernelization dichotomies for hitting minors un der structural parameterizations» DTSTART;VALUE=DATE-TIME:20251023T080000Z DTEND;VALUE=DATE-TIME:20251023T084500Z DTSTAMP;VALUE=DATE-TIME:20250930T185115Z UID:6f7cd66b-68ac-4f33-89d6-473622557eb8 SEQUENCE:0 CREATED;VALUE=DATE-TIME:20250930T185115Z DESCRIPTION:For a finite collection of connected graphs F\, the F-Minor De letion problem consists in\, given a graph G and an integer l\, deciding w hether G contains a vertex set of size at most l whose removal results in an F-minor-free graph. We lift the existence of approximate polynomial ker nels for F-Minor Deletion by the solution size to approximate polynomial k ernels parameterized by the vertex-deletion distance to graphs of bounded elimination distance to F-minor-free graphs. This results in exact polynom ial kernels for every family F that contains a planar graph\, and an appro ximate polynomial kernel for Planar Vertex Deletion. Moreover\, combining our result with a previous lower bound\, we obtain the following infinite set of dichotomies\, assuming NP is not contained in coNP/poly: for any fi nite set F of biconnected graphs on at least three vertices containing a p lanar graph\, and any minor-closed class of graphs C\, F-Minor Deletion ad mits a polynomial kernel parameterized by the vertex-deletion distance to C if and only if C has bounded elimination distance to F-minor-free graphs . For instance\, this yields dichotomies for Cactus Vertex Deletion\, Oute rplanar Vertex Deletion\, and Treewidth-t Vertex Deletion for every intege r t ≥ 0. Prior to our work\, such dichotomies were only known for the pa rticular cases of Vertex Cover and Feedback Vertex Set. Our approach build s on the techniques developed by Jansen and Pieterse [Theor. Comput. Sci. 2020] and also uses adaptations of some of the results by Jansen\, de Kroo n\, and Wlodarczyk [STOC 2021].\n\nJoint work with Marin Bougeret and Igna si Sau. LAST-MODIFIED;VALUE=DATE-TIME:20251022T080103Z LOCATION:Bât 4\, E.3.23. URL:https://info-web.lirmm.fr/collorg/6f7cd66b-68ac-4f33-89d6-473622557eb8 END:VEVENT BEGIN:VEVENT SUMMARY:Eunjung Kim\, «Twin-width and the algorithmic implications» DTSTART;VALUE=DATE-TIME:20220331T080000Z DTEND;VALUE=DATE-TIME:20220331T090000Z DTSTAMP;VALUE=DATE-TIME:20220309T103821Z UID:b0725238-8455-497d-a711-8234f57ecb57 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20220309T103821Z DESCRIPTION:A contraction sequence of a graph consists of iteratively merg ing two of its vertices until only one vertex remains. The recently introd uced graph invariant called the twin-width is based on contraction sequenc es [BKTW\, J. ACM ’22]. More precisely\, if one puts error edges\, hence forth red edges\, between two vertices representing non-homogeneous subset s\, the twin-width is the minimum integer d such that a contraction sequen ce\, called d-sequence\, exists that keeps red degree at most d. Many well -known graph classes are shown to have bounded twin-width including unit i nterval graphs\, a strict hereditary class of permutation graphs\, posets of bounded width\, proper minor-closed class\, subgraphs of O(1)-dimension al grids as well as graphs of bounded tree-width and clique-width. Since i ts introduction two years ago\, twin-width gained extensive traction acros s areas such as graph theory\, algorithms design\, logic\, data structure\ , constraint programming and communication complexity. \n\nIn this talk\, we review some algorithmic implications of twin-width on graphs of bounded twin-width and beyond such graphs. \n\nIt was proved in [BKTW\, JACM ’2 2] that FO (first-order) model-checking is fixed-parameter tractable provi ded that a d-sequence is given. This unifies and extends known tractabilit y results. Due to its generality\, the running time of FO model-checking a lgorithm suffers a huge dependency on the (nested) quantifier depth of the input sentence. It turns out that for concrete well-known problems such a s k-Dominating Set\, k-Independent Set and Subgraph Isomorphism in general \, slick dynamic programming can be designed so that the runtime dependenc y is single exponential in k provided O(1)-sequence is given [BGKTW\, ICAL P ’21]. The spirit of such DP algorithms is further extended in [BKRT\, SODA ’22] to attain an alternative proof for the tractability MSO model- checking on graph of bounded clique-width [Courcelle\, Makowsky\, Rotics\, TCS ’00].\n\nThe terrain of monotone (closed under taking subgraphs) gr aph classes is fully charted in regards to fixed-parameter tractability of FO model-checking: a monotone graph class is nowhere dense if and only if FO model-checking is fpt on it. For the more general hereditary (closed u nder taking induced subgraphs) graph classes\, it is conjectured that a cl ass admits an fpt algorithm for FO model-checking if and only the class “does not encode all finite graphs in a manner interpretable by FO logi c” (monadically dependent). We survey a few graph classes where the conj ecture is positively affirmed and the dividing line is drawn precisely by the twin-width. Such classes include ordered graphs [BGdMST\, STOC ’22]\ , permutation graphs [BKTW\, JACM ’22] and circle graphs [Hlinený\, Fil ip Pokrývka\, '22]\, interval graphs and rooted directed path graphs [BCK KLT\, ’22]. \n\nTwin-width can be useful for designing algorithms even o n graph classes of unbounded twin-width. Some structures like large bicliq ues\, half-graphs\, or independent sets are responsible for making the twi n-width large on the main classes of intersection and visibility graphs. C ombined with the FPT algorithm for FO model checking on graphs given with O(1)-sequences\, this give rise to a variety of algorithmic win-win argume nts [BCKKLT\, ’22]. For instance\, we readily derive fpt algorithms for k-Independent Set on visibility graphs of simple polygons\, which was addr essed as an open problem LAST-MODIFIED;VALUE=DATE-TIME:20220330T080103Z LOCATION:https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/b0725238-8455-497d-a711-8234f57ecb57 END:VEVENT BEGIN:VEVENT SUMMARY:Clement Rambaud\, «Excluding a rectangular grid» DTSTART;VALUE=DATE-TIME:20251106T090000Z DTEND;VALUE=DATE-TIME:20251106T100000Z DTSTAMP;VALUE=DATE-TIME:20251023T135251Z UID:ac09d85d-c124-4640-bea2-aa29a524a3a4 SEQUENCE:0 CREATED;VALUE=DATE-TIME:20251023T135251Z DESCRIPTION:For every positive integer k\, we define the k-treedepth as th e largest graph parameter td_k satisfying (i) td_k(∅)=0\; (ii) td_k(G) < = 1+td_k(G-u) for every graph G and for every vertex u\; and (iii) if G is a (= |V(G)|. We prove that for every positive integer k\, a class of graphs C has bounded k-treedepth if and on ly if there is a positive integer l such that for every tree T on k vertic es\, no graph in C contains T□ P_l as a minor. This unifies known result s on treedepth\, and 2-treedepth (Huynh\, Joret\, Micek\, Seweryn\, and Wo llan\; 2021). Moreover\, we deduce that graphs excluding the k x l grid as a minor have bounded (2k-1)-treedepth\, which is a qualitative strengthen ing of the Grid-Minor Theorem (Robertson and Seymour).\nThis talk is based on https://arxiv.org/abs/2501.11617. LAST-MODIFIED;VALUE=DATE-TIME:20251105T090103Z LOCATION:E3.24 URL:https://info-web.lirmm.fr/collorg/ac09d85d-c124-4640-bea2-aa29a524a3a4 END:VEVENT BEGIN:VEVENT SUMMARY:Maximilian Gorsky\, «Matching Theory\, Hamiltonicity\, and Barnet te's Conjecture» DTSTART;VALUE=DATE-TIME:20220519T080000Z DTEND;VALUE=DATE-TIME:20220519T090000Z DTSTAMP;VALUE=DATE-TIME:20220309T130824Z UID:28b92e35-2f5d-46d8-8431-a5e323b29fc8 SEQUENCE:7 CREATED;VALUE=DATE-TIME:20220309T130824Z DESCRIPTION:Barnette's Conjecture claims that all cubic\, 3-connected\, pl anar\, bipartite graphs are Hamiltonian. We give a translation of this con jecture into the matching-theoretic setting. This allows us to relax the r equirement of planarity to give the equivalent conjecture that all cubic\, 3-connected\, Pfaffian\, bipartite graphs are Hamiltonian.\n\nA graph is a brace if it is bipartite and any two disjoint edges are part of a perfec t matching. Our perspective allows us to observe that Barnette's Conjectur e can be reduced to cubic\, planar braces. We show a similar reduction to braces for cubic\, 3-connected\, bipartite graphs regarding four stronger versions of Hamiltonicity. Note that in these cases we do not need planari ty. As a practical application of these results\, we provide some suppleme nts to a generation procedure for cubic\, 3-connected\, planar\, bipartite graphs discovered by Holton et al. [Hamiltonian Cycles in Cubic 3-Connect ed Bipartite Planar Graphs\, JCTB\, 1985]. These allow us to check whether a graph we generated is a brace.\n\nJoint work with Sebastian Wiederrecht und Raphael Steiner. LAST-MODIFIED;VALUE=DATE-TIME:20220518T080103Z LOCATION:https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/28b92e35-2f5d-46d8-8431-a5e323b29fc8 END:VEVENT BEGIN:VEVENT SUMMARY:Nofar Carmeli\, «Query answering: tractability beyond acyclicity » DTSTART;VALUE=DATE-TIME:20230323T090000Z DTEND;VALUE=DATE-TIME:20230323T090000Z DTSTAMP;VALUE=DATE-TIME:20230306T075851Z UID:ad089688-686f-4f19-b9b8-e66333906f94 SEQUENCE:1 CREATED;VALUE=DATE-TIME:20230306T075851Z DESCRIPTION:Consider the task of enumerating the answers to natural join q ueries over databases.\nGiven a join query\, it is known that this can be done with ideal time guarantees (linear preprocessing and constant delay) iff the query is alpha-acyclic\, under some fine-grained complexity assump tions. In the first part of the talk\, we will inspect how the non-acyclic case can be handled\, and in particular consider the affect of self-joins and endomorphisms in the query graph on the complexity. In the second par t\, we will consider more demanding query-answering tasks and see how to e xtend the requirements from the query structure beyond acyclicity to suppo rt these tasks efficiently. LAST-MODIFIED;VALUE=DATE-TIME:20230322T090102Z LOCATION:E.3.23 Bâtiment 4 LIRMM\, https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/ad089688-686f-4f19-b9b8-e66333906f94 END:VEVENT BEGIN:VEVENT SUMMARY:Lucas Isenmann\, «Diviser les sommets d'un graphe pour en faire u ne union de 2-clubs» DTSTART;VALUE=DATE-TIME:20260226T090000Z DTEND;VALUE=DATE-TIME:20260226T100000Z DTSTAMP;VALUE=DATE-TIME:20260126T101536Z UID:9827a44a-e774-4bdc-a881-822411c5190b SEQUENCE:1 CREATED;VALUE=DATE-TIME:20260126T101536Z DESCRIPTION:Un problème classique consiste à supprimer des sommets d'un graphe jusqu'à ce qu'il devienne une union de cliques. Minimiser le nombr e de supprimer est alors NP-difficile. D'autres variantes ont été étudi és : en changeant les opérations (ajout ou suppression d'arêtes)\, en c herchant à ce que le graphe vérifie certaines propriétés. Notre sujet de recherche à été d'étudier l'opération de division de sommets (ou v ertex splitting) consistant à remplacer un sommet par deux sommets de sor te que chaque voisin du sommet original soit adjacent à au moins un des d eux sommets. Nous avons étudié la complexité pour minimiser le nombre d e splits pour faire du graphe une union de 2-clubs. On verra que ce probl ème est NP-difficile\, FPT et APX-hard. LAST-MODIFIED;VALUE=DATE-TIME:20260225T091602Z LOCATION:E.3.23 URL:https://info-web.lirmm.fr/collorg/9827a44a-e774-4bdc-a881-822411c5190b END:VEVENT BEGIN:VEVENT SUMMARY:Elisabet Burjons\, «Lower Bounds for Conjunctive and Disjunctive Turing Kernels» DTSTART;VALUE=DATE-TIME:20220317T090000Z DTEND;VALUE=DATE-TIME:20220317T100000Z DTSTAMP;VALUE=DATE-TIME:20220118T170614Z UID:06a5d372-f5d4-4f45-8bf5-117d505b1820 SEQUENCE:3 CREATED;VALUE=DATE-TIME:20220118T170614Z DESCRIPTION:The non-existence of polynomial kernels for OR- and AND-compos itional problems is now a well-established result. Some of these problems have adaptive or non-adaptive polynomial Turing kernels. Up to now\, most known polynomial Turing kernels are non-adaptive and most of them are of t he conjunctive or disjunctive kind. For some problems it has been conjectu red that the existence of polynomial Turing kernels is unlikely. For insta nce\, either all or none of the WK[1]-complete problems have polynomial Tu ring kernels. While it has been conjectured that they do not\, a proof tyi ng their non-existence to some complexity theoretic assumption is still mi ssing and seems to be beyond the reach of today’s standard techniques.\n We proved that OR-compositional problems and all WK[1]-hard problems do no t have conjunctive polynomial kernels\, a special type of non-adaptive Tur ing kernels\, under the assumption that coNP ⊈ NP/poly. Similarly\, it i s unlikely that AND-compositional problems have disjunctive polynomial ker nels. Moreover\, we present a way to prove that the parameterized versions of some ⊕ P-hard problems\, for instance\, Odd Path on planar graphs\, do not have conjunctive or disjunctive polynomial kernels\, unless coNP ⊆ NP/poly.\n\nJoint work with Peter Rossmanith LAST-MODIFIED;VALUE=DATE-TIME:20220316T090102Z LOCATION:https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/06a5d372-f5d4-4f45-8bf5-117d505b1820 END:VEVENT BEGIN:VEVENT SUMMARY:Giannos Stamoulis\, «Paths and Cycles of Large Rank in Frameworks » DTSTART;VALUE=DATE-TIME:20220324T090000Z DTEND;VALUE=DATE-TIME:20220324T090000Z DTSTAMP;VALUE=DATE-TIME:20220128T163950Z UID:6183f73e-caeb-47ad-8bfd-19efc2c3ccd1 SEQUENCE:3 CREATED;VALUE=DATE-TIME:20220128T163950Z DESCRIPTION:We provide fixed-parameter tractable (FPT) algorithms for the following generalization of the fundamental Longest Path and Longest Cycle problems. Following Lovász\, we call by a //framework// a pair $(G\,M)$\ , where $G$ is an undirected graph and $M$ is a matroid whose elements are the vertices of $G$. Then for a framework $(G\,M)$ and integer $k$\, the Max Rank Path/Cycle problem asks whether there is a path/cycle in $G$ whos e vertices form a set of rank at least $k$ in $M$. \nMax Rank Path/Cycle e ncompasses several fundamental problems about paths and cycles in graphs. When $M$ is a uniform matroid of rank $|V(G)|$\, then Max Rank Path/Cycle becomes the problem of finding a path (or cycle) with at least $k$ vertice s\, one of the most studied problems in parameterized complexity. Other no table special cases of Max Rank Path/Cycle are the problems of finding a c ycle containing at least $k$ terminal vertices and a path in a colored gra ph containing at least $k$ different colors. \nThe main results of our pap er are two theorems about Max Rank Path/Cycle. The first theorem gives a r andomized FPT algorithm when matroid $M$ is representable over a finite fi eld (with parameter $k$ and the order of the field). This implies\, for ex ample\, the first FPT algorithm for finding a path containing at least $k$ different colors. The second theorem establishes a deterministic FPT algo rithm for planar graphs and matroids representable over finite fields or r ationals.\n\nJoint work with Fedor V. Fomin\, Petr A. Golovach\, Tuukka Ko rhonen. LAST-MODIFIED;VALUE=DATE-TIME:20220323T090102Z LOCATION:https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/6183f73e-caeb-47ad-8bfd-19efc2c3ccd1 END:VEVENT BEGIN:VEVENT SUMMARY:William Lochet\, «Minimum-Membership Geometric Set Cover for unit squares» DTSTART;VALUE=DATE-TIME:20230316T090000Z DTEND;VALUE=DATE-TIME:20230316T100000Z DTSTAMP;VALUE=DATE-TIME:20230310T143956Z UID:4997faf6-9daa-487b-8911-cd38377ebf36 SEQUENCE:0 CREATED;VALUE=DATE-TIME:20230310T143956Z DESCRIPTION:The minimum-membership set cover (MMSC) problem is a variant o f the traditional set cover problem. Given a universe S and a collection o f sets R\, the goal of MMSC is to select a subset R of R such that every e lement in S is covered by R. Instead of minimizing the size of R as in the usual set cover problem\, the goal of MMSC is to minimize the maximum deg ree of an element of S in R. This problem was introduced by Kuhn et al. in 2005\, where they gave a log(n) approximation in polynomial time and show ed that it was the best approximation ratio we could hope for under standa rd complexity assumptions.\nIn this talk\, we will focus on the problem wh ere the sets S and R represent geometric objects. This setting was first s tudied by Erlebach and van Leeuwen in 2008\, where they showed NP-hardness for approximating the problem with a ratio less than 2 on unit disks and unit squares. They also gave a 5-approximation algorithm that runs in poly nomial time when OPT is bounded (n^O(OPT)) for the case of unit squares. T he main goal of the talk will be to present a constant factor approximatio n algorithm that runs in (truly) polynomial time.\n\nThis is based on join t work with S. Bandyapadhyay\, S. Saurabh\, and J. Xue. LAST-MODIFIED;VALUE=DATE-TIME:20230315T090103Z LOCATION:E.3.23 Bâtiment 4 LIRMM\, https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/4997faf6-9daa-487b-8911-cd38377ebf36 END:VEVENT BEGIN:VEVENT SUMMARY:Jean Florent Raymond\, «Long induced paths in minor-closed graph classes and beyond» DTSTART;VALUE=DATE-TIME:20220407T080000Z DTEND;VALUE=DATE-TIME:20220407T090000Z DTSTAMP;VALUE=DATE-TIME:20220308T142751Z UID:cf14420f-d589-42e5-a3f5-e892da26dfeb SEQUENCE:4 CREATED;VALUE=DATE-TIME:20220308T142751Z DESCRIPTION:In this paper we show that every graph of pathwidth less than k that has a path of order n also has an induced path of order at least $\ \frac{1}{3}n^{1/k}$. This is an exponential improvement and a generalizati on of the polylogarithmic bounds obtained by Esperet\, Lemoine and Maffray (2016) for interval graphs of bounded clique number. We complement this r esult with an upper-bound.\nThis result is then used to prove the two foll owing generalizations:\n- every graph of treewidth less than k that has a path of order n contains an induced path of order at least $\\frac{1}{4}(\ \log n)^{1/k}$\;\n- for every non-trivial graph class that is closed under topological minors there is a constant $d∈(0\,1)$ such that every graph from this class that has a path of order n contains an induced path of or der at least $(\\log n)^d$.\nWe also describe consequences of these result s beyond graph classes that are closed under topological minors.\n\nJoint work with Claire Hilaire. LAST-MODIFIED;VALUE=DATE-TIME:20220406T080102Z LOCATION:https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/cf14420f-d589-42e5-a3f5-e892da26dfeb END:VEVENT BEGIN:VEVENT SUMMARY:Dibyayan Chakraborty\, «Approximation of isometric path cover» DTSTART;VALUE=DATE-TIME:20220630T083000Z DTEND;VALUE=DATE-TIME:20220630T090000Z DTSTAMP;VALUE=DATE-TIME:20220616T190023Z UID:cc63d579-1be7-412f-b528-22eaac249812 SEQUENCE:4 CREATED;VALUE=DATE-TIME:20220616T190023Z DESCRIPTION:This talk about an algorithmic problem called Isometric Path C over\, where the objective is to cover the vertices of a graph using small est number of isometric paths. We show that the problem is NP-hard even on chordal graphs and provide constant factor approximation algorithms for g raphs with bounded tree-length. LAST-MODIFIED;VALUE=DATE-TIME:20220629T083102Z LOCATION:BAT4 l Séminaire LIRMM - RDC URL:https://info-web.lirmm.fr/collorg/cc63d579-1be7-412f-b528-22eaac249812 END:VEVENT BEGIN:VEVENT SUMMARY:Michał Włodarczyk\, «Lossy Planarization: A Constant-Factor App roximate Kernelization for Planar Vertex Deletion» DTSTART;VALUE=DATE-TIME:20220414T080000Z DTEND;VALUE=DATE-TIME:20220414T080000Z DTSTAMP;VALUE=DATE-TIME:20220110T092924Z UID:f7f747c8-c822-4707-abb7-23d71f403cbd SEQUENCE:10 CREATED;VALUE=DATE-TIME:20220110T092924Z DESCRIPTION:In the $\\mathcal{F}$-minor-free deletion problem we want to f ind a minimum vertex set in a given graph that intersects all minor models of graphs from the family $\\mathcal{F}$. The Vertex planarization proble m is a special case of $\\mathcal{F}$-minor-free deletion for the family $ \\mathcal{F} = {K_5\, K_{3\,3}}$. Whenever the family $\\mathcal{F}$ conta ins at least one planar graph\, then $\\mathcal{F}$-minor-free deletion is known to admit a constant-factor approximation algorithm and a polynomial kernelization [Fomin\, Lokshtanov\, Misra\, and Saurabh\, FOCS'12]. The V ertex planarization problem is arguably the simplest setting for which $\\ mathcal{F}$ does not contain a planar graph and the existence of a constan t-factor approximation or a polynomial kernelization remains a major open problem.\nIn this work we show that Vertex planarization admits an algorit hm which is a combination of both approaches. Namely\, we present a polyno mial $A$-approximate kernelization\, for some constant $A > 1$\, based on the framework of lossy kernelization [Lokshtanov\, Panolan\, Ramanujan\, a nd Saurabh\, STOC'17]. Simply speaking\, when given a graph $G$ and intege r $k$\, we show how to compute a graph $G'$ on $\\mathsf{poly}(k)$ vertice s so that any $B$-approximate solution to $G'$ can be lifted to an $(A\\cd ot B)$-approximate solution to $G$\, as long as $A\\cdot B\\cdot {\\rm OP T}(G) ≤ k$. In order to achieve this\, we develop a framework for sparsi fication of planar graphs which approximately preserves all separators and near-separators between subsets of the given terminal set. Our result yie lds an improvement over the state-of-art approximation algorithms for Vert ex planarization. The problem admits a polynomial-time $O(n^ε)$-approxima tion algorithm\, for any $ε > 0$\, and a quasi-polynomial-time $(\\log n) ^{O(1)}$ approximation algorithm\, both randomized [Kawarabayashi and Sidi ropoulos\, FOCS'17]. By pipelining these algorithms with our approximate k ernelization\, we improve the approximation factors to respectively $O({\\ rm OPT}^ε)$ and $(\\log {\\rm OPT})^{O(1)}$.\n\nJoint work with Bart Jans en LAST-MODIFIED;VALUE=DATE-TIME:20220413T080103Z LOCATION:https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/f7f747c8-c822-4707-abb7-23d71f403cbd END:VEVENT BEGIN:VEVENT SUMMARY:Alexandre Talon\, «The complexity of colouring graphs without C4' s or stable sets of size 4: a story with a C++ program» DTSTART;VALUE=DATE-TIME:20230330T080000Z DTEND;VALUE=DATE-TIME:20230330T090000Z DTSTAMP;VALUE=DATE-TIME:20230314T180133Z UID:775632b6-3d4c-4d8b-9710-2995729e2523 SEQUENCE:0 CREATED;VALUE=DATE-TIME:20230314T180133Z DESCRIPTION:In this talk\, we present a work in progress about the complex ity of proper colouring in hereditary classes of graphs. This problem\, ce ntral in structural graph theory\, is known to be NP-complete in the gener al case. We will focus on the colouring problem restricted to the classes of graphs defined by a set of forbidden induced subgraphs.\nAs Lozin and M alyshev recall in Vertex coloring of graphs with few obstructions\, when t he set H contains only graphs with 4 vertices there are only 3 remaining m inimal classes of graphs for which the complexity of the colouring problem is still unknown. We study here one of these classes: the class of graphs containing neither cycles of size 4 nor stables of size 4\, denoted by\, Free{C4\, 4K1}.\nIn (2P2\, K4)-Free Graphs are 4-colorable\, Gaspers and H uang showed that this class contains only graphs which can be covered by a t most 4 cliques. According to the clique covering number\, the problem sh ows different facets: easy if 2-cliques colourable\, but harder otherwise. \nWe present here our partial results concerning the harder case. To tackl e it\, we use two complementary approaches: one theoretical\, dealing with the concepts of clique-width\, and one consisting in enumerating and reco gnising interesting structures using a computer program.\nThis talk could also mention enumerating graphs being the intersection of rectangles\, if the audience wants to know about this.\n\nThis is a joint work with Cléop hée Robin and Marco Caoduro LAST-MODIFIED;VALUE=DATE-TIME:20230329T080102Z LOCATION:E.3.23 Bâtiment 4 LIRMM\, https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/775632b6-3d4c-4d8b-9710-2995729e2523 END:VEVENT BEGIN:VEVENT SUMMARY:Timothé Picavet\, «Locally approximating dominating sets in K_{2 \,t}-minor-free graphs» DTSTART;VALUE=DATE-TIME:20231005T083000Z DTEND;VALUE=DATE-TIME:20231005T090000Z DTSTAMP;VALUE=DATE-TIME:20230928T125123Z UID:5d603080-de4c-4033-b809-755fdae5693c SEQUENCE:3 CREATED;VALUE=DATE-TIME:20230928T125123Z DESCRIPTION:The field of distributed algorithms studies algorithms that ar e designed to run on different computers simultaneously\, without any shar ed memory. We focus on the so-called LOCAL model\, where computers are par t of a network and work together to solve a problem (in our case Minimum D ominating Set) on the network itself. The LOCAL model is used to study the locality in network computing\, to determine which problems can be solved when every computer only knows a part of the network (in our case a const ant radius region) before outputting. As finding a constant-factor approxi mation of MDS is not possible on general graphs\, we will focus on minor f orbidden classes\, particularly the class of $K_{2\,t}$-minor-free graphs. We give a $(2t-1)$-approximation for MDS on this class\, which breaks the non-exponential approximation factor barrier. This also generalizes and s implifies the involved proof of the 5 approximation factor for outerplanar graphs. LAST-MODIFIED;VALUE=DATE-TIME:20231004T083103Z LOCATION:BAT4 l Séminaire (LIRMM - RDC Entrée) URL:https://info-web.lirmm.fr/collorg/5d603080-de4c-4033-b809-755fdae5693c END:VEVENT BEGIN:VEVENT SUMMARY:Hugo Jacob\, «On the parameterized complexity of computing tree-p artitions» DTSTART;VALUE=DATE-TIME:20230406T080000Z DTEND;VALUE=DATE-TIME:20230406T090000Z DTSTAMP;VALUE=DATE-TIME:20230316T190754Z UID:789d3874-9ed8-4b23-947c-d616df33559d SEQUENCE:1 CREATED;VALUE=DATE-TIME:20230316T190754Z DESCRIPTION:Following some recent FPT algorithms parameterized by the widt h of a given tree-partition due to Bodlaender\, Cornelissen\, and van der Wegen\, we consider the parameterized problem of computing a decomposition . We prove that computing an optimal tree-partition is XALP-complete\, whi ch is likely to exclude FPT algorithms. However\, we prove that computing a tree-partition of approximate width is tractable using a relatively simp le sketch. This is sufficient to remove the requirement of having a\ngiven tree-partition for FPT algorithms. Our simple sketch can be adapted for s everal regimes within polynomial time and FPT time. Furthermore\, we adapt some simple structural results about the tree-partition width of subdivis ions\, and use them to compare tree-cut width and tree-partition width.\n\ nBased on joint work with Hans Bodlaender and Carla Groenland. LAST-MODIFIED;VALUE=DATE-TIME:20230405T080103Z LOCATION:E.3.23 Bâtiment 4 LIRMM\, https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/789d3874-9ed8-4b23-947c-d616df33559d END:VEVENT BEGIN:VEVENT SUMMARY:Raul Wayne\, «Adapting the Directed Grid Theorem into an FPT algo rithm» DTSTART;VALUE=DATE-TIME:20220428T080000Z DTEND;VALUE=DATE-TIME:20220428T090000Z DTSTAMP;VALUE=DATE-TIME:20220421T205108Z UID:1fa15e5b-7600-45a0-805f-ffe1399d3206 SEQUENCE:3 CREATED;VALUE=DATE-TIME:20220421T205108Z DESCRIPTION:The Grid Theorem of Robertson and Seymour [JCTB\, 1986] is one of the most important tools in the field of structural graph theory\, fin ding numerous applications in the design of algorithms for undirected grap hs. An analogous version of the Grid Theorem in digraphs was conjectured b y Johnson et al. [JCTB\, 2001]\, and proved by Kawarabayashi and Kreutzer [STOC\, 2015]. They showed that there is a function $f(k)$ such that every digraph of directed tree-width at least $f(k)$ contains a cylindrical gri d of order $k$ as a butterfly minor. Their constructive proof can be turne d into an XP algorithm\, with parameter $k$\, that either constructs a dec omposition of the appropriate width or finds the claimed large cylindrical grid as a butterfly minor.\n\nIn this talk\, we present the ideas we used to adapt the Directed Grid Theorem into an FPT algorithm. We provide two FPT algorithms with parameter $k$. The first one either produces an arbore al decomposition of width $3k-2$ or finds a $(k-1)$-linked set in a digrap h $D$\, improving on the original result for arboreal decompositions by Jo hnson et al. [JCTB\, 2001]. The second one uses a bramble B that naturally occurs in digraphs of large directed tree-width to find a well-linked set of order k whose vertices appear in a path hitting all elements of $B$. A s a tool to prove these results\, we also show how to solve a generalized version of the problem of finding balanced separators for a set of vertice s $T$ in FPT time with parameter $|T|$.\n\nJoint work with Victor Campos\, Ana Karolinna Maia\, and Ignasi Sau. LAST-MODIFIED;VALUE=DATE-TIME:20221118T154047Z LOCATION:https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/1fa15e5b-7600-45a0-805f-ffe1399d3206 END:VEVENT BEGIN:VEVENT SUMMARY:Stavros Kolliopoulos\, «Precedence-Constrained Covering Problems with Multiplicity Constraints» DTSTART;VALUE=DATE-TIME:20220616T080000Z DTEND;VALUE=DATE-TIME:20220616T090000Z DTSTAMP;VALUE=DATE-TIME:20220418T112023Z UID:8a5e4cc2-91e5-4e6f-acab-59a18b740b82 SEQUENCE:7 CREATED;VALUE=DATE-TIME:20220418T112023Z DESCRIPTION:We study the approximability of covering problems when the set of\nitems chosen to satisfy the covering constraints must be a prefix of a\ngiven partial order. We examine the general case with multiplicity\ncon straints\, where item $i$ can be chosen up to $d_i$ times. For the\nbasic Precedence-Constrained Knapsack problem (PCKP) we answer an open\nquestion of McCormick et al. and show the existence of approximation\nalgorithms w ith strongly-polynomial bounds.\n\nPCKP is a special case\, with a single covering constraint\, of a\nPrecedence-Constrained Covering Integer Progra m (PCCP). For a general\nPCCP where the number of covering constraints is $m \\geq 1\,$ we show\nthat an algorithm of Pritchard and Chakrabarty for Covering Integer\nPrograms can be extended to yield an $f$-approximation\, where $f$ is\nthe maximum number of variables with nonzero coefficients i n a\ncovering constraint. This is nearly-optimal under standard\ncomplexit y-theoretic assumptions and rather surprisingly matches the\nbound known f or the problem without precedence constraints.\n\n\nJoint work with Antoni s Skarlatos. LAST-MODIFIED;VALUE=DATE-TIME:20220615T080103Z LOCATION:Bât 4\, salle du séminaire (LIRMM - RDC Entrée) URL:https://info-web.lirmm.fr/collorg/8a5e4cc2-91e5-4e6f-acab-59a18b740b82 END:VEVENT BEGIN:VEVENT SUMMARY:Mathieu Mari\, «Shortest Disjoint Paths on a Grid» DTSTART;VALUE=DATE-TIME:20240321T090000Z DTEND;VALUE=DATE-TIME:20240321T100000Z DTSTAMP;VALUE=DATE-TIME:20240229T102701Z UID:f79d7b59-d5ba-450f-9ea9-b0a66514ead3 SEQUENCE:3 CREATED;VALUE=DATE-TIME:20240229T102701Z DESCRIPTION:The well-known k-disjoint paths problem involves finding pairw ise\nvertex-disjoint paths between k specified pairs of vertices within a\ ngiven graph if they exist. In the shortest k-disjoint paths problem one\n looks for such paths of minimum total length. Despite nearly 50 years of\n active research on the k-disjoint paths problem\, many open problems and\n complexity gaps still persist. A particularly well-defined scenario\,\nins pired by VLSI design\, focuses on infinite rectangular grids where the\nte rminals are placed at arbitrary grid points. While the decision\nproblem i n this context remains NP-hard\, no prior research has provided\nany posit ive results for the optimization version. In this talk I\npresent a fixed- parameter tractable (FPT) algorithm for this scenario.\nIt is important to stress that this is the first result achieving the\nFPT complexity of the shortest disjoint paths problem in any\, even very\nrestricted classes of graphs where we do not put any restriction on the\nplacements of the term inals.\n\nThe talk will end with some open questions related to the shorte st\ndisjoint paths problem. This result appears in SODA'24. \n\nJoint work with Anish Mukherjee\, Michal Pilipczuk and Piotr Sankowski. LAST-MODIFIED;VALUE=DATE-TIME:20240320T090102Z LOCATION:E.3.24 Bâtiment 4 LIRMM URL:https://info-web.lirmm.fr/collorg/f79d7b59-d5ba-450f-9ea9-b0a66514ead3 END:VEVENT BEGIN:VEVENT SUMMARY:Lars Jaffke\, «A logic-based algorithmic meta-theorem for mim-wid th» DTSTART;VALUE=DATE-TIME:20220602T080000Z DTEND;VALUE=DATE-TIME:20220602T090000Z DTSTAMP;VALUE=DATE-TIME:20220309T213109Z UID:c4f8d4e8-a165-4365-80f8-9eb008bdaaed SEQUENCE:1 CREATED;VALUE=DATE-TIME:20220309T213109Z DESCRIPTION:We introduce a logic called distance neighborhood logic with a cyclicity and connectivity constraints (A&C DN for short) which extends ex istential MSO1 with predicates for querying neighborhoods of vertex sets a nd for verifying connectivity and acyclicity of vertex sets in various pow ers of a graph. Building upon [Bergougnoux and Kanté\, ESA 2019\; SIDMA 2 021]\, we show that the model checking problem for every fixed A&C DN form ula is solvable in n^O(w) time when the input graph is given together with a branch decomposition of mim-width w. Nearly all problems that are known to be solvable in polynomial time given a branch decomposition of constan t mim-width can be expressed in this framework. We add several natural pro blems to this list\, including problems asking for diverse sets of solutio ns.\n\nOur model checking algorithm is efficient whenever the given branch decomposition of the input graph has small index in terms of the d-neighb orhood equivalence [Bui-Xuan\, Telle\, and Vatshelle\, TCS 2013]. We there fore unify and extend known algorithms for tree-width\, clique-width and r ank-width. Our algorithm has a single-exponential dependence on these thre e width measures and asymptotically matches run times of the fastest known algorithms for several problems. This results in algorithms with tight ru n times under the Exponential Time Hypothesis (ETH) for tree-width and cli que-width\; the above mentioned run time for mim-width is nearly tight und er the ETH for several problems as well. Our results are also tight in ter ms of the expressive power of the logic: we show that already slight exten sions of our logic make the model checking problem para-NP-hard when param eterized by mim-width plus formula length.\n\nJoint work with Benjamin Ber gougnoux and Jan Dreier. LAST-MODIFIED;VALUE=DATE-TIME:20220601T080102Z LOCATION:https://www.lirmm.fr/algco/GT/zoom URL:https://info-web.lirmm.fr/collorg/c4f8d4e8-a165-4365-80f8-9eb008bdaaed END:VEVENT BEGIN:VEVENT SUMMARY:Cléophée Robin\, «A Closure Lemma for tough graphs and Hamilton ian degree conditions (14h30)» DTSTART;VALUE=DATE-TIME:20230420T123000Z DTEND;VALUE=DATE-TIME:20230420T123000Z DTSTAMP;VALUE=DATE-TIME:20230328T140021Z UID:d7c421fb-f818-4a59-98cc-4809aa40a755 SEQUENCE:2 CREATED;VALUE=DATE-TIME:20230328T140021Z DESCRIPTION:A graph G is hamiltonian if it exists a cycle in G containing all vertices of G exactly once. A graph G is t-tough if\, for all subsets of vertices S\, the number of connected components in G − S is at most | S| / t. We extended the Theorem of Hoàng by proving the following : Let G be a graph with degree sequence d_1\,d_2\,…\,d_n and let t be a positiv e integer at most 4. If G is t-tough and if. ∀ i\, t ≤ i