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PRODID:-//Discrete Mathematics Group - ECPv6.15.20//NONSGML v1.0//EN
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X-ORIGINAL-URL:https://dimag.ibs.re.kr
X-WR-CALDESC:Events for Discrete Mathematics Group
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X-Robots-Tag:noindex
X-PUBLISHED-TTL:PT1H
BEGIN:VTIMEZONE
TZID:Asia/Seoul
BEGIN:STANDARD
TZOFFSETFROM:+0900
TZOFFSETTO:+0900
TZNAME:KST
DTSTART:20200101T000000
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END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220427T163000
DTEND;TZID=Asia/Seoul:20220427T173000
DTSTAMP:20260418T010215
CREATED:20220427T073000Z
LAST-MODIFIED:20240705T173041Z
UID:5399-1651077000-1651080600@dimag.ibs.re.kr
SUMMARY:Michael Savery\, Induced subgraphs of induced subgraphs of large chromatic number
DESCRIPTION:We prove that for every graph F with at least one edge there are graphs H of arbitrarily large chromatic number and the same clique number as F such that every F-free induced subgraph of H has chromatic number at most c=c(F). (Here a graph is F-free if it does not contain an induced copy of F.) This generalises recent theorems of Briański\, Davies and Walczak\, and of Carbonero\, Hompe\, Moore and Spirkl. We further show an analogous statement where clique number is replaced by odd girth. This is joint work with Antonio Girão\, Freddie Illingworth\, Emil Powierski\, Alex Scott\, Youri Tamitegama and Jane Tan.
URL:https://dimag.ibs.re.kr/event/2022-04-27/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220413T163000
DTEND;TZID=Asia/Seoul:20220413T173000
DTSTAMP:20260418T010215
CREATED:20220413T073000Z
LAST-MODIFIED:20240707T080102Z
UID:5378-1649867400-1649871000@dimag.ibs.re.kr
SUMMARY:Jakub Gajarský\, Model Checking on Interpretations of Classes of Bounded Local Clique-Width
DESCRIPTION:The first-order model checking problem for finite graphs asks\, given a graph G and a first-order sentence $\phi$ as input\, to decide whether $\phi$ holds on G. Showing the existence of an efficient algorithm for this problem implies the existence of efficient parameterized algorithms for various commonly studied problems\, such as independent set\, distance-r dominating set\, and many others. \nWhile the first-order model-checking problem is likely not efficiently solvable in general\, efficient algorithms exist for various restricted graph classes\, such as graphs of bounded degree\, planar graphs etc. After the existence of an efficient model checking algorithm was shown for nowhere dense classes of graphs (which include most of commonly studied classes of sparse graphs)\, the attention turned to the more general setting of graph classes which can be obtained from sparse graphs using graph transformations called interpretations/transductions. However\, despite efforts of several groups of researchers\, no positive algorithmic result has been achieved since 2016\, when the existence of an efficient algorithm was shown for graph classes interpretable in graphs of bounded degree. \nWe present a fixed-parameter tractable algorithm for first-order model checking on interpretations of graph classes with bounded local clique-width. Notably\, this includes interpretations of planar graphs (and more generally\, of locally bounded treewidth) and vastly generalizes the result for interpretations of graphs of bounded degree. To obtain this result we developed a new tool which works in a very general setting of dependent classes and which we believe can be an important ingredient in achieving similar results in the future. \nThis is joint work with Édouard Bonnet\, Jan Dreier\, Stephan Kreutzer\, Nikolas Mählmann\, Pierre Simon\, Szymon Toruńczyk.
URL:https://dimag.ibs.re.kr/event/2022-04-13/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220330T163000
DTEND;TZID=Asia/Seoul:20220330T173000
DTSTAMP:20260418T010215
CREATED:20220330T073000Z
LAST-MODIFIED:20240707T080136Z
UID:5270-1648657800-1648661400@dimag.ibs.re.kr
SUMMARY:Jean-Florent Raymond\, Long induced paths in minor-closed graph classes and beyond
DESCRIPTION:In 1982 Galvin\, Rival\, and Sands proved that in $K_{t\,t}$-subgraph free graphs (t being fixed)\, the existence of a path of order n guarantees the existence of an induced path of order f(n)\, for some (slowly) increasing function f. The problem of obtaining good lower-bounds for f for specific graph classes was investigated decades later and logarithmic bounds have been obtained for planar graphs (more generally for graphs of bounded genus) and for interval graphs. \nIn this talk I will show that every graph of pathwidth less than k that has a path of order n also has an induced path of order $Ω(n^{1/k})$. I will then explain how this result can be used to prove the two following generalizations: \n\nevery graph of treewidth less than k that has a path of order n contains an induced path of order $Ω((\log n)^{1/k})$;\nfor 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 order $Ω((\log n)^d)$.\n\nJoint work with Claire Hilaire.
URL:https://dimag.ibs.re.kr/event/2022-03-30/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220310T163000
DTEND;TZID=Asia/Seoul:20220310T173000
DTSTAMP:20260418T010215
CREATED:20220310T073000Z
LAST-MODIFIED:20240705T174146Z
UID:5176-1646929800-1646933400@dimag.ibs.re.kr
SUMMARY:Fedor Fomin\, Long cycles in graphs: Extremal Combinatorics meets Parameterized Algorithms
DESCRIPTION:We examine algorithmic extensions of two classic results of extremal combinatorics. First\, the theorem of Dirac from 1952 asserts that a 2-connected graph G with the minimum vertex degree d>1\, is either Hamiltonian or contains a cycle of length at least 2d. Second\, the theorem of Erdős-Gallai from 1959\, states that a 2-connected graph G with the average vertex degree D>1\, contains a cycle of length at least D. \nWe discuss the recent progress in parameterized complexity of computing long cycles “above” the guarantees established by these classical theorems: cycles of lengths at least 2d+k and D+k. \nThe talk is based on the joint works with Petr Golovach\, Danil Sagunov\, and Kirill Simonov.
URL:https://dimag.ibs.re.kr/event/2022-03-10/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220218T100000
DTEND;TZID=Asia/Seoul:20220218T110000
DTSTAMP:20260418T010215
CREATED:20220218T010000Z
LAST-MODIFIED:20240705T174212Z
UID:5154-1645178400-1645182000@dimag.ibs.re.kr
SUMMARY:Manuel Lafond\, Recognizing k-leaf powers in polynomial time\, for constant k
DESCRIPTION:A graph G is a k-leaf power if there exists a tree T whose leaf set is V(G)\, and such that uv is an edge if and only if the distance between u and v in T is at most k. The graph classes of k-leaf powers have several applications in computational biology\, but recognizing them has remained a challenging algorithmic problem for the past two decades. In a recent paper presented at SODA22\, it was shown that k-leaf powers can be recognized in polynomial time if k is fixed. \nIn this seminar\, I will present the algorithm that decides whether a graph G is a k-leaf power in time $O(n^{f(k)})$ for some function f that depends only on k (but has the growth rate of a power tower function). More specifically\, I will discuss how the difficult k-leaf power instances contain many cutsets that have the same neighborhood layering. I will then show that these similar cutsets are redundant and that removing one of them does not lose any information\, which can be exploited for algorithmic purposes.
URL:https://dimag.ibs.re.kr/event/2022-02-18/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220210T163000
DTEND;TZID=Asia/Seoul:20220210T173000
DTSTAMP:20260418T010215
CREATED:20220210T073000Z
LAST-MODIFIED:20240707T080439Z
UID:5183-1644510600-1644514200@dimag.ibs.re.kr
SUMMARY:James Davies\, Separating polynomial $\chi$-boundedness from $\chi$-boundedness
DESCRIPTION:We prove that there is a function $f : \mathbb{N} \to \mathbb{N}$ such that for every function $g : \mathbb{N} \to \mathbb{N} \cup \{\infty\}$ with $g(1)=1$ and $g \ge f$\, there is a hereditary class of graphs $\mathcal{G}$ such that for each $\omega \in \mathbb{N}$\, the maximum chromatic number of a graph in $\mathcal{G}$ with clique number $\omega$ is equal to $g(\omega)$. This extends a recent breakthrough of Carbonero\, Hompe\, Moore\, and Spirk. In particular\, this proves that there are hereditary classes of graphs that are $\chi$-bounded but not polynomially $\chi$-bounded. \nJoint work with Marcin Briański and Bartosz Walczak.
URL:https://dimag.ibs.re.kr/event/2022-02-10/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220127T163000
DTEND;TZID=Asia/Seoul:20220127T173000
DTSTAMP:20260418T010215
CREATED:20211230T013247Z
LAST-MODIFIED:20240705T180010Z
UID:5080-1643301000-1643304600@dimag.ibs.re.kr
SUMMARY:Bo Ning (宁博)\, Substructures and eigenvalues of graphs: Triangles and quadrilaterals
DESCRIPTION:Our talk will mainly focus on the relationship between substructures and eigenvalues of graphs. We will briefly survey recent developments on a conjecture of Bollobás and Nikiforov and a classical result of Nosal on triangles. In particular\, we shall present counting results for previous spectral theorems on triangles and quadrilaterals. If time allows\, we will give a sketch for the proof of one new counting result on triangles.
URL:https://dimag.ibs.re.kr/event/2022-01-27/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220120T163000
DTEND;TZID=Asia/Seoul:20220120T173000
DTSTAMP:20260418T010215
CREATED:20220120T073000Z
LAST-MODIFIED:20240705T175100Z
UID:4564-1642696200-1642699800@dimag.ibs.re.kr
SUMMARY:Ken-ichi Kawarabayashi (河原林 健一)\, Toward Directed Graph Minor Theory
DESCRIPTION:Graph Minor project by Robertson and Seymour is perhaps the deepest theory in Graph Theory. It gives a deep structural characterization of graphs without any graph $H$ as a minor. It also gives many exciting algorithmic consequences. \nIn this work\, I would like to talk about our attempt to extend Graph minor project to directed graphs. Topics include \n1. The directed grid theorem\n2. The directed flat wall theorem\n3. Tangle tree decomposition\n4. Variant of the directed disjoint paths problems\n5. Toward the structure (and decomposition) theorem for H-minor-free digraphs. \nJoint work with Stephan Kreutzer\, O-joung Kwon\, Archontia Giannopoulou.
URL:https://dimag.ibs.re.kr/event/2022-01-20/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220113T163000
DTEND;TZID=Asia/Seoul:20220113T173000
DTSTAMP:20260418T010215
CREATED:20220113T073000Z
LAST-MODIFIED:20240707T080528Z
UID:5009-1642091400-1642095000@dimag.ibs.re.kr
SUMMARY:Ron Aharoni\, A strong version of the Caccetta-Haggkvist conjecture
DESCRIPTION:The Caccetta-Haggkvist conjecture\, one of the best known in graph theory\, is that in a digraph with $n$ vertices in which all outdegrees are at least $n/k$ there is a directed cycle of length at most $k$. This is known for  large values of $k$\, relatively to n\, and asymptotically for n large. A few years ago I offered a generalization: given sets $F_1$\, $\ldots$\, $F_n$ of sets of undirected edges\, each of size at least $n/k$\, there exists a rainbow undirected cycle of length  at most $k$. The directed version is obtained by taking as $F_i$ the set of edges going out of the vertex $v_i$ ($i \le n$)\, with the directions removed. I will tell about recent results on this conjecture\, obtained together with He Guo\, with Beger\, Chudnovsky and Zerbib\, and with DeVos and Holzman.
URL:https://dimag.ibs.re.kr/event/2022-01-13/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211209T163000
DTEND;TZID=Asia/Seoul:20211209T173000
DTSTAMP:20260418T010215
CREATED:20211209T073000Z
LAST-MODIFIED:20240705T180040Z
UID:4671-1639067400-1639071000@dimag.ibs.re.kr
SUMMARY:David Munhá Correia\, Rainbow matchings
DESCRIPTION:I will discuss various results for rainbow matching problems. In particular\, I will introduce a ‘sampling trick’ which can be used to obtain short proofs of old results as well as to solve asymptotically some well known conjectures. This is joint work with Alexey Pokrovskiy and Benny Sudakov.
URL:https://dimag.ibs.re.kr/event/2021-12-09/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211125T163000
DTEND;TZID=Asia/Seoul:20211125T173000
DTSTAMP:20260418T010215
CREATED:20211125T073000Z
LAST-MODIFIED:20240705T181009Z
UID:4552-1637857800-1637861400@dimag.ibs.re.kr
SUMMARY:Tuukka Korhonen\, Fast FPT-Approximation of Branchwidth
DESCRIPTION:Branchwidth determines how graphs\, and more generally\, arbitrary connectivity (basically symmetric and submodular) functions could be decomposed into a tree-like structure by specific cuts. We develop a general framework for designing fixed-parameter tractable (FPT) 2-approximation algorithms for branchwidth of connectivity functions. The first ingredient of our framework is combinatorial. We prove a structural theorem establishing that either a sequence of particular refinement operations could decrease the width of a branch decomposition or that the width of the decomposition is already within a factor of 2 from the optimum. The second ingredient is an efficient implementation of the refinement operations for branch decompositions that support efficient dynamic programming. We present two concrete applications of our general framework. \n\nAn algorithm that for a given n-vertex graph G and integer k in time $2^{2^{O(k)}} n^2$ either constructs a rank decomposition of G of width at most 2k or concludes that the rankwidth of G is more than $k$. It also yields a $(2^{2k+1}−1)$-approximation algorithm for cliquewidth within the same time complexity\, which in turn\, improves to $f(k) n^2$ the running times of various algorithms on graphs of cliquewidth $k$. Breaking the “cubic barrier” for rankwidth and cliquewidth was an open problem in the area.\nAn algorithm that for a given n-vertex graph G and integer k in time $2^{O(k)} n$ either constructs a branch decomposition of G of width at most $2k$ or concludes that the branchwidth of G is more than $k$. This improves over the 3-approximation that follows from the recent treewidth 2-approximation of Korhonen [FOCS 2021].\n\nThis is joint work with Fedor Fomin.
URL:https://dimag.ibs.re.kr/event/2021-11-25/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211111T163000
DTEND;TZID=Asia/Seoul:20211111T173000
DTSTAMP:20260418T010215
CREATED:20211111T073000Z
LAST-MODIFIED:20240705T181024Z
UID:4668-1636648200-1636651800@dimag.ibs.re.kr
SUMMARY:Sebastian Wiederrecht\, Matching Minors in Bipartite Graphs
DESCRIPTION:Matching minors are a specialisation of minors which preserves the existence and elementary structural properties of perfect matchings. They were first discovered as part of the study of the Pfaffian recognition problem on bipartite graphs (Polya’s Permanent Problem) and acted as a major inspiration for the definition of butterfly minors in digraphs. In this talk we consider the origin and motivation behind the study of matching minors\, the current state of the art\, and their relation to structural digraph theory. The main result is a generalisation of the structure theorem by Robertson et al. and McCuaig for $K_{3\,3}$-matching minor free bipartite graphs to bipartite graphs excluding $K_{t\,t}$ as a matching minor for general t. This generalisation can be seen as a matching theoretic version of the Flat Wall Theorem by Robertson and Seymour.
URL:https://dimag.ibs.re.kr/event/2021-11-11/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211105T163000
DTEND;TZID=Asia/Seoul:20211105T173000
DTSTAMP:20260418T010215
CREATED:20211105T073000Z
LAST-MODIFIED:20240707T080839Z
UID:4555-1636129800-1636133400@dimag.ibs.re.kr
SUMMARY:Martin Milanič\, Tree Decompositions with Bounded Independence Number
DESCRIPTION:The independence number of a tree decomposition $\mathcal{T}$ of a graph is the smallest integer $k$ such that each bag of $\mathcal{T}$ induces a subgraph with independence number at most $k$. If a graph $G$ is given together with a tree decomposition with bounded independence number\, then the Maximum Weight Independent Set (MWIS) problem can be solved in polynomial time. Motivated by this observation\, we consider six graph containment relations—the subgraph\, topological minor\, and minor relations\, as well 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. Furthermore\, using a variety of tools including SPQR trees and potential maximal cliques\, we show how to obtain such tree decompositions efficiently. \nAs an immediate consequence\, we obtain that the MWIS problem can be solved in polynomial time in an infinite family of graph classes that properly contain the class of chordal graphs. In fact\, our approach shows that the Maximum Weight Independent $\mathcal{H}$-Packing problem\, a common generalization of the MWIS and the Maximum Weight Induced Matching problems\, can be solved in polynomial time in these graph classes. \nThis is joint work with Clément Dallard and Kenny Štorgel.
URL:https://dimag.ibs.re.kr/event/2021-11-05/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211008T100000
DTEND;TZID=Asia/Seoul:20211008T110000
DTSTAMP:20260418T010215
CREATED:20211008T010000Z
LAST-MODIFIED:20240707T080932Z
UID:4450-1633687200-1633690800@dimag.ibs.re.kr
SUMMARY:Paul Seymour\, Polynomial bounds for chromatic number
DESCRIPTION:The Gyárfás-Sumner conjecture says that for every forest $H$\, there is a function $f$ such that the chromatic number $\chi(G)$ is at most $f(\omega(G))$ for every $H$-free graph $G$ (“$H$-free” means with no induced subgraph isomorphic to $H$\, and $\omega(G)$ is the size of the largest clique of $G$). This well-known conjecture has been proved only for a few types of forest. \nNevertheless\, there is a much stronger conjecture\, due to Esperet: that for every forest $H$\, there is a polynomial function $f$ as above. As one might expect\, this has been proved for even fewer types of forest; and the smallest tree $H$ for which Esperet’s conjecture is not known is the five-vertex path $P_5$. \nA third notorious conjecture is the Erdős-Hajnal conjecture\, that for every graph $H$\, there exists $c>0$ such that $\alpha(G)\omega(G)\ge |G|^c$ for every $H$-free graph $G$ (where $\alpha(G)$ is the size of the largest stable set of $G$). The smallest graph $H$ for which this is not known is also $P_5$\, which\, conveniently\, is a forest; and every forest that satisfies Esperet’s conjecture also satisfies the Erdős-Hajnal conjecture. So there is substantial interest in the chromatic numbers of $P_5$-free graphs. The best upper bound that was previously known\, due to Esperet\, Lemoine\, Maffray\, and Morel\, was that $\chi(G)\le (5/27)3^\omega(G)$ for every $P_5$-free graph $G$ with $\omega(G) > 2$. In recent work with Alex Scott and Sophie Spirkl\, we have proved several results related to Esperet’s conjecture\, including proofs of its truth for some new types of forest $H$\, and a “near-polynomial” bound when $H = P_5$\, that $\chi(G) \le \omega(G)^{\log_2(\omega(G))}$ for every $P_5$-free graph $G$ with $\omega(G) > 2$. We survey these results and give a proof of the new bound for $P_5$.
URL:https://dimag.ibs.re.kr/event/2021-10-08/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210930T163000
DTEND;TZID=Asia/Seoul:20210930T173000
DTSTAMP:20260418T010215
CREATED:20210930T073000Z
LAST-MODIFIED:20240707T080948Z
UID:4460-1633019400-1633023000@dimag.ibs.re.kr
SUMMARY:Péter Pál Pach\, The Alon-Jaeger-Tarsi conjecture via group ring identities
DESCRIPTION:The Alon-Jaeger-Tarsi conjecture states that for any finite field $\mathbb{F}$ of size at least 4  and any nonsingular matrix $M$ over $\mathbb{F}$ there exists a vector $x$ such that neither $x$ nor $Mx$ has a 0 component. In joint work with János Nagy we proved this conjecture when the size of the field is sufficiently large\, namely\, when $61
URL:https://dimag.ibs.re.kr/event/2021-09-30/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210818T170000
DTEND;TZID=Asia/Seoul:20210818T180000
DTSTAMP:20260418T010215
CREATED:20210818T080000Z
LAST-MODIFIED:20240705T182104Z
UID:4353-1629306000-1629309600@dimag.ibs.re.kr
SUMMARY:Petr Hliněný\, Twin-width is linear in the poset width
DESCRIPTION:Twin-width is a new parameter informally measuring how diverse are the neighbourhoods of the graph vertices\, and it extends also to other binary relational structures\, e.g. to digraphs and posets. It was introduced quite recently\, in 2020 by Bonnet\, Kim\, Thomassé\, and Watrigant. One of the core results of these authors is that FO model checking on graph classes of bounded twin-width is in FPT. With that result\, they also claimed that posets of bounded width have bounded twin-width\, thus capturing a prior result on FO model checking of posets of bounded width in FPT. However\, their translation from poset width to twin-width was indirect and giving only a very loose double-exponential bound. \nWe prove that posets of width d have twin-width at most 9d with a direct and elementary argument\, and show that this bound is tight up to a constant factor. Specifically\, for posets of width 2\, we prove that in the worst case their twin-width is also equal to 2. These two theoretical results are complemented with straightforward algorithms to construct the respective contraction sequence for a given poset. \n(Joint work with my student Jakub Balaban who obtained the main ideas in his bachelor thesis.)
URL:https://dimag.ibs.re.kr/event/2021-08-18/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210728T150000
DTEND;TZID=Asia/Seoul:20210728T160000
DTSTAMP:20260418T010215
CREATED:20210607T135955Z
LAST-MODIFIED:20240705T184022Z
UID:4228-1627484400-1627488000@dimag.ibs.re.kr
SUMMARY:Maria Chudnovsky\, Induced subgraphs and tree decompositions
DESCRIPTION:Tree decompositions are a powerful tool in structural graph theory; they are traditionally used in the context of forbidden graph minors. Connecting tree decompositions and forbidden induced subgraphs has until recently remained out of reach. \nTree decompositions are closely related to the existence of  “laminar collections of separations” in a graph\, which roughly means that the separations in the collection “cooperate” with each other\, and the pieces that are obtained when the graph is simultaneously decomposed by all the separations in the collection “line up” to form a tree structure. Such collections of separations come up naturally in the context of forbidden minors. \nIn the case of families where induced subgraphs are excluded\, while there are often natural separations\, they are  usually very far from forming a laminar collection. In what follows we mostly focus on families of graphs of bounded degree. It turns out that due to the bound on the degree\, these collections of natural separations can be partitioned into a bounded number of laminar collections. This in turn allows to us obtain a wide variety of structural and algorithmic results\, which we will survey in this talk.
URL:https://dimag.ibs.re.kr/event/2021-07-28/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210714T170000
DTEND;TZID=Asia/Seoul:20210714T180000
DTSTAMP:20260418T010215
CREATED:20210615T091821Z
LAST-MODIFIED:20240705T184018Z
UID:4257-1626282000-1626285600@dimag.ibs.re.kr
SUMMARY:Stefan Weltge\, Integer programs with bounded subdeterminants and two nonzeros per row
DESCRIPTION:We give a strongly polynomial-time algorithm for integer linear programs defined by integer coefficient matrices whose subdeterminants are bounded by a constant and that contain at most two nonzero entries in each row. The core of our approach is the first polynomial-time algorithm for the weighted stable set problem on graphs that do not contain more than k vertex-disjoint odd cycles\, where k is any constant. Previously\, polynomial-time algorithms were only known for k=0 (bipartite graphs) and for k=1. \nWe observe that integer linear programs defined by coefficient matrices with bounded subdeterminants and two nonzeros per column can be also solved in strongly polynomial-time\, using a reduction to b-matching. \nThis is joint work with Samuel Fiorini\, Gwenaël Joret\, and Yelena Yuditsky.
URL:https://dimag.ibs.re.kr/event/2021-07-14/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210630T170000
DTEND;TZID=Asia/Seoul:20210630T180000
DTSTAMP:20260418T010215
CREATED:20210617T062135Z
LAST-MODIFIED:20240707T081259Z
UID:4277-1625072400-1625076000@dimag.ibs.re.kr
SUMMARY:Florian Gut and Attila Joó\, Large vertex-flames in uncountable digraphs
DESCRIPTION:The local connectivity  $ \kappa_D(r\,v) $ from $ r $ to $ v $ is defined to be the maximal number of internally disjoint $r\rightarrow v $ paths in $ D $. A spanning subdigraph $ L $ of $ D $ with $  \kappa_L(r\,v)=\kappa_D(r\,v) $ for every $ v\in V-r $ must have at least $ \sum_{v\in V-r}\kappa_D(r\,v) $ edges. It was shown by Lovász that\, maybe surprisingly\, this lower bound is sharp for every finite digraph. The optimality of an $ L $ can be captured by the following characterization: For every $ v\in V-r $ there is a system $ \mathcal{P}_v $ of internally disjoint $ r\rightarrow v $ paths in $ L $ covering all the ingoing edges of $ v $ in $ L $ such that one can choose from  each $ P\in \mathcal{P}_v $ either an edge or an internal vertex in such a way that the resulting set meets every $ r\rightarrow v $ path of $ D $. We prove that every digraph of size at most $ \aleph_1 $  admits such a spanning subdigraph $ L $. The question if this remains true for larger digraphs remains open.
URL:https://dimag.ibs.re.kr/event/2021-06-30/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210616T170000
DTEND;TZID=Asia/Seoul:20210616T180000
DTSTAMP:20260418T010215
CREATED:20210428T010009Z
LAST-MODIFIED:20240705T184215Z
UID:4020-1623862800-1623866400@dimag.ibs.re.kr
SUMMARY:Alan Lew\, Representability and boxicity of simplicial complexes
DESCRIPTION:An interval graph is the intersection graph of a family of intervals in the real line. Motivated by problems in ecology\, Roberts defined the boxicity of a graph G to be the minimal k such that G can be written as the intersection of k interval graphs. \nA natural higher-dimensional generalization of interval graphs is the class d-representable complexes. These are simplicial complexes that carry the information on the intersection patterns of a family of convex sets in $mathbb R^d$. We define the d-boxicity of a simplicial complex X to be the minimal k such that X can be written as the intersection of k d-representable complexes. \nA classical result of Roberts\, later rediscovered by Witsenhausen\, asserts that the boxicity of a graph with n vertices is at most n/2. Our main result is the following high dimensional extension of Roberts’ theorem: Let X be a simplicial complex on n vertices with minimal non-faces of dimension at most d. Then\, the d-boxicity of X is at most $frac{1}{d+1}binom{n}{d}$. \nExamples based on Steiner systems show that our result is sharp. The proofs combine geometric and topological ideas.
URL:https://dimag.ibs.re.kr/event/2021-06-16/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210602T170000
DTEND;TZID=Asia/Seoul:20210602T180000
DTSTAMP:20260418T010215
CREATED:20210506T022454Z
LAST-MODIFIED:20240705T184206Z
UID:4042-1622653200-1622656800@dimag.ibs.re.kr
SUMMARY:Adam Zsolt Wagner\, Constructions in combinatorics via neural networks
DESCRIPTION:Recently\, significant progress has been made in the area of machine learning algorithms\, and they have quickly become some of the most exciting tools in a scientist’s toolbox. In particular\, recent advances in the field of reinforcement learning have led computers to reach superhuman level play in Atari games and Go\, purely through self-play. In this talk\, I will give a very basic introduction to neural networks and reinforcement learning algorithms. I will also indicate how these methods can be adapted to the “game” of trying to find a counterexample to a mathematical conjecture\, and show some examples where this approach was successful.
URL:https://dimag.ibs.re.kr/event/2021-06-02/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210526T170000
DTEND;TZID=Asia/Seoul:20210526T180000
DTSTAMP:20260418T010215
CREATED:20210424T122241Z
LAST-MODIFIED:20240707T081338Z
UID:3986-1622048400-1622052000@dimag.ibs.re.kr
SUMMARY:Dimitrios M. Thilikos\, Bounding Obstructions sets: the cases of apices of minor closed classes
DESCRIPTION:Given a minor-closed graph class ${\cal G}$\, the (minor) obstruction of ${\cal G}$ is the set of all minor-minimal graphs not in ${\cal G}$. Given a non-negative integer $k$\, we define the $k$-apex of ${\cal A}$ as the class containing every graph $G$ with a set $S$ of vertices whose removal from $G$ gives a graph on ${\cal G}$. We prove that every obstruction of the $k$-apex of ${\cal G}$ has size bounded by some 4-fold exponential function of $p(k)$ where p is a polynomial function whose degree depends on the size of the minor-obstructions of ${\cal G}$. This bound drops to a 2-fold exponential one when ${\cal G}$ excludes some apex graph as a minor (i.e.\, a graph in the $1$-apex of planar graphs). \nJoint work with Ignasi Sau and Giannos Stamoulis.
URL:https://dimag.ibs.re.kr/event/2021-05-26/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210521T170000
DTEND;TZID=Asia/Seoul:20210521T180000
DTSTAMP:20260418T010215
CREATED:20210319T050153Z
LAST-MODIFIED:20240705T190024Z
UID:3818-1621616400-1621620000@dimag.ibs.re.kr
SUMMARY:Benjamin Bumpus\, Directed branch-width: A directed analogue of tree-width
DESCRIPTION:Many problems that are NP-hard in general become tractable on `structurally recursive’ graph classes. For example\, consider classes of bounded tree- or clique-width. Since the 1990s\, many directed analogues of tree-width have been proposed. However\, many natural problems (e.g. directed HamiltonPath and MaxCut) remain intractable on such digraph classes of `bounded width’. \nIn this talk\, I will introduce a new tree-width analogue for digraphs called directed branch-width which allows us to define digraph classes for which many problems (including directed HamiltonPath and MaxCut)  become linear-time solvable. Furthermore\, via the definition of directed branch-width\, I will obtain a generalisation to digraphs of Gurski and Wanke’s characterization of graph classes of bounded tree-width in terms of their line graphs. \nThis is joint work with Kitty Meeks and William Pettersson.
URL:https://dimag.ibs.re.kr/event/2021-05-21/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210512T170000
DTEND;TZID=Asia/Seoul:20210512T180000
DTSTAMP:20260418T010215
CREATED:20210319T045925Z
LAST-MODIFIED:20240705T190026Z
UID:3816-1620838800-1620842400@dimag.ibs.re.kr
SUMMARY:Johannes Carmesin\, A Whitney type theorem for surfaces: characterising graphs with locally planar embeddings
DESCRIPTION:Given a graph\, how do we construct a surface so that the graph embeds in that surface in an optimal way? Thomassen showed that for minimum genus as optimality criterion\, this problem would be NP-hard. Instead of minimum genus\, here we use local planarity — and provide a polynomial algorithm. \nOur embedding method is based on Whitney’s trick to use matroids to construct embeddings in the plane. Consequently we obtain a characterisation of the graphs admitting locally planar embeddings in surfaces in terms of a certain matroid being co-graphic.
URL:https://dimag.ibs.re.kr/event/2021-05-12/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210506T100000
DTEND;TZID=Asia/Seoul:20210506T110000
DTSTAMP:20260418T010215
CREATED:20210319T045807Z
LAST-MODIFIED:20240705T190027Z
UID:3813-1620295200-1620298800@dimag.ibs.re.kr
SUMMARY:Raul Lopes\, Adapting the Directed Grid Theorem into an FPT Algorithm
DESCRIPTION:The Grid Theorem of Robertson and Seymour [JCTB\, 1986] is one of the most important tools in the field of structural graph theory\, finding numerous applications in the design of algorithms for undirected graphs. An analogous version of the Grid Theorem in digraphs was conjectured by 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 grid of order k as a butterfly minor and stated that their proof can be turned into an XP algorithm\, with parameter k\, that either constructs a decomposition of the appropriate width\, or finds the claimed large cylindrical grid as a butterfly minor. \nIn this talk\, we present the ideas used in our adaptation of the Directed Grid Theorem into an FPT algorithm. We provide two FPT algorithms with parameter k. The first one either produces an arboreal decomposition of width 3k-2 or finds a haven of order k in a digraph D. 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 that is contained in the set of vertices of a path hitting all elements of B. As tools to prove these results\, we show how to solve a generalized version of the problem of finding balanced separators for a given set of vertices T in FPT time with parameter |T|. \nJoint work with Victor Campos\, Ana Karolinna Maia\, and Ignasi Sau.
URL:https://dimag.ibs.re.kr/event/2021-05-06/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210421T170000
DTEND;TZID=Asia/Seoul:20210421T180000
DTSTAMP:20260418T010215
CREATED:20210414T142646Z
LAST-MODIFIED:20240705T185049Z
UID:3936-1619024400-1619028000@dimag.ibs.re.kr
SUMMARY:Reinhard Diestel\, Tangles of set separations: a novel clustering method and type recognition in machine learning
DESCRIPTION:Traditional clustering identifies groups of objects that share certain qualities. Tangles do the converse: they identify groups of qualities that typically occur together. They can thereby discover\, relate\, and structure types: of behaviour\, political views\, texts\, or proteins. Tangles offer a new\, quantitative\, paradigm for grouping phenomena rather than things. They can identify key phenomena that allow predictions of others. Tangles also offer a new paradigm for clustering in large data sets.  \nThe mathematical theory of tangles has its origins in the theory of graph minors developed by Robertson and Seymour. It has recently been axiomatized in a way that makes it applicable to a wide range of contexts outside mathematics: from clustering in data science to predicting customer behaviour in economics\, from DNA sequencing and drug development to text analysis and machine learning. \nThis very informal talk will not show you the latest intricacies of abstract tangle theory (for which you can find links on the tangle pages of my website)\, but to win you over to join our drive to develop real tangle applications in areas as indicated above. We have some software to share\, but are looking for people to try it out with us on real-world examples! \nHere are some introductory pages from a book I am writing on this\, which may serve as an extended abstract: https://arxiv.org/abs/2006.01830
URL:https://dimag.ibs.re.kr/event/2021-04-21/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210414T170000
DTEND;TZID=Asia/Seoul:20210414T180000
DTSTAMP:20260418T010215
CREATED:20210301T235620Z
LAST-MODIFIED:20240707T081558Z
UID:3698-1618419600-1618423200@dimag.ibs.re.kr
SUMMARY:István Tomon\, Ramsey properties of semilinear graphs
DESCRIPTION:A graph $G$ is semilinear of bounded complexity if the vertices of $G$ are elements of $\mathbb{R}^{d}$\, and the edges of $G$ are defined by the sign patterns of $t$ linear functions\, where $d$ and $t$ are constants. In this talk\, I will present several results about the symmetric and asymmetric Ramsey properties of semilinear graphs. Some interesting instances of such graphs are intersection graphs of boxes\, interval overlap graphs\, and shift graphs\, so our results extend several well known theorems about the Ramsey and coloring properties of these geometrically defined graphs.
URL:https://dimag.ibs.re.kr/event/2021-04-14/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210407T170000
DTEND;TZID=Asia/Seoul:20210407T180000
DTSTAMP:20260418T010215
CREATED:20210301T235812Z
LAST-MODIFIED:20240705T190042Z
UID:3701-1617814800-1617818400@dimag.ibs.re.kr
SUMMARY:Michał Pilipczuk\, Structural properties of powers of sparse graphs
DESCRIPTION:For a graph G and an integer d\, the dth power of G is the graph $G^d$ on the same vertex set as G where two vertices are considered adjacent if and only if they are at distance at most d in G. Assuming that G is sparse\, what can we say about the structure in $G^d$? Certainly $G^d$ can be dense\, as the square of a star is a complete graph\, but $G^d$ still retains many properties that can be derived from the sparsity of G. We will present some recent results in this spirit\, in particular connected to colorings and to the Erdős-Hajnal property\, assuming that G is drawn from a fixed class of bounded expansion or from a fixed nowhere dense class. The talk will be based on the recent papers: “Clustering Powers of Sparse Graphs” (with J. Nešetřil\, P. Ossona de Mendez\, and X. Zhu) and “Erdős-Hajnal properties for powers of sparse graphs” (with M. Briański\, P. Micek\, and M. Seweryn).
URL:https://dimag.ibs.re.kr/event/2021-04-07/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210401T100000
DTEND;TZID=Asia/Seoul:20210401T110000
DTSTAMP:20260418T010215
CREATED:20210218T001134Z
LAST-MODIFIED:20240705T191014Z
UID:3642-1617271200-1617274800@dimag.ibs.re.kr
SUMMARY:Sophie Spirkl\, Pure pairs in ordered graphs
DESCRIPTION:A pure pair in a graph G is a pair of subsets A\, B of the vertex set of G such that in G\, either all of the edges or none of the edges between A and B are present. Pure pairs have been studied recently motivated by their connections to the Erdos-Hajnal conjecture. \nIn this talk\, I will discuss the topic of pure pairs in ordered graphs\, that is\, graphs with a linear ordering on their vertex set. If we exclude a graph H as an ordered induced subgraph\, how large a pure pair can we guarantee? I will talk about how the answer differs from the case of unordered graphs and show some of the techniques used. \nBased on joint work with Maria Chudnovsky\, Jacob Fox\, Alex Scott\, and Paul Seymour.
URL:https://dimag.ibs.re.kr/event/2021-04-01/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210324T170000
DTEND;TZID=Asia/Seoul:20210324T180000
DTSTAMP:20260418T010215
CREATED:20210219T024236Z
LAST-MODIFIED:20240705T191012Z
UID:3649-1616605200-1616608800@dimag.ibs.re.kr
SUMMARY:Édouard Bonnet\, Twin-width and ordered binary structures
DESCRIPTION:The twin-width of a graph G can be defined as the least integer d such that there is a sequence of length |V(G)| of (strictly) coarser 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-width of ordered binary structures\, or if you prefer\, matrices on a finite alphabet. This turns out to be key in understanding combinatorial\, algorithmic\, and model-theoretic properties of (hereditary) classes of those objects. We will see several characterizations of bounded twin-width for these classes. The main consequences in the three domains read as follows. \n\nEnumerative combinatorics: All the classes of 0\,1-matrices with superexponential growth have growth at least n! (in turn resolving a conjecture of Balogh\, Bollobás\, and Morris on the growth of hereditary classes of ordered graphs).\nAlgorithms: First-order model checking of ordered binary structures is tractable exactly when the twin-width is bounded.\nFinite model theory: Monadically-dependent and dependent hereditary classes of ordered binary structures are the same.\n\nIn addition we get a fixed-parameter algorithm approximating matrix twin-width within a function of the optimum\, which is still missing for unordered graphs. \nJoint work with Ugo Giocanti\, Patrice Ossona de Mendez\, and Stéphan Thomassé. Similar results have been obtained independently by Pierre Simon and Szymon Toruńczyk.
URL:https://dimag.ibs.re.kr/event/2021-03-24/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
END:VCALENDAR