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X-WR-CALNAME:Discrete Mathematics Group
X-ORIGINAL-URL:https://dimag.ibs.re.kr
X-WR-CALDESC:Events for Discrete Mathematics Group
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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:20220125T163000
DTEND;TZID=Asia/Seoul:20220125T173000
DTSTAMP:20260417T160759
CREATED:20220125T073000Z
LAST-MODIFIED:20240705T175100Z
UID:5129-1643128200-1643131800@dimag.ibs.re.kr
SUMMARY:O-joung Kwon (권오정)\, Reduced bandwidth: a qualitative strengthening of twin-width in minor-closed classes (and beyond)
DESCRIPTION:In a reduction sequence of a graph\, vertices are successively identified until the graph has one vertex. At each step\, when identifying $u$ and $v$\, each edge incident to exactly one of $u$ and $v$ is coloured red. Bonnet\, Kim\, Thomassé\, and Watrigant [FOCS 2020] defined the twin-width of a graph $G$ to be the minimum integer $k$ such that there is a reduction sequence of $G$ in which every red graph has maximum degree at most $k$. For any graph parameter $f$\, we define the reduced-$f$ of a graph $G$ to be the minimum integer $k$ such that there is a reduction sequence of $G$ in which every red graph has $f$ at most $k$. Our focus is on graph classes with bounded reduced-bandwidth\, which implies and is stronger than bounded twin-width (reduced-maximum-degree). \nWe show that every proper minor-closed class has bounded reduced-bandwidth\, which is qualitatively stronger than a result of Bonnet et al. for bounded twin-width. In many instances\, we also make quantitative improvements. For example\, all previous upper bounds on the twin-width of planar graphs were at least $2^{1000}$. We show that planar graphs have reduced-bandwidth at most $466$ and twin-width at most $583$; moreover\, the witnessing reduction sequence can be constructed in polynomial time. We show that $d$-powers of graphs in a proper minor-closed class have bounded reduced-bandwidth (irrespective of the degree of the vertices). \nThis is joint work with Édouard bonnet and David Wood.
URL:https://dimag.ibs.re.kr/event/2022-01-25/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220120T163000
DTEND;TZID=Asia/Seoul:20220120T173000
DTSTAMP:20260417T160759
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:20220118T163000
DTEND;TZID=Asia/Seoul:20220118T173000
DTSTAMP:20260417T160759
CREATED:20220118T073000Z
LAST-MODIFIED:20240707T080518Z
UID:5105-1642523400-1642527000@dimag.ibs.re.kr
SUMMARY:Jaehyeon Seo (서재현)\, A rainbow Turán problem for color-critical graphs
DESCRIPTION:For given $k$ graphs $G_1\,\dots\, G_k$ over a common vertex set of size $n$\, what conditions on $G_i$ ensures a ‘colorful’ copy of $H$\, i.e. a copy of $H$ containing at most one edge from each $G_i$? \nKeevash\, Saks\, Sudakov\, and Verstraëte defined $\operatorname{ex}_k(n\,H)$ to be the maximum total number of edges of the graphs $G_1\,\dots\, G_k$ on a common vertex set of size $n$ having no colorful copy of $H$. They completely determined $\operatorname{ex}_k(n\,K_r)$ for large $n$ by showing that\, depending on the value of $k$\, one of the two natural constructions is always the extremal construction. Moreover\, they conjectured the same holds for every color-critical graphs and proved it for $3$-color-critical graphs. \nWe prove their conjecture for $4$-color-critical graphs and for almost all $r$-color-critical graphs when $r > 4$. Moreover\, we show that for every non-color-critical non-bipartite graphs\, none of the two natural constructions is extremal for certain values of $k$. This is a joint work with Debsoumya Chakraborti\, Jaehoon Kim\, Hyunwoo Lee\, and Hong Liu.
URL:https://dimag.ibs.re.kr/event/2022-01-18/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220113T163000
DTEND;TZID=Asia/Seoul:20220113T173000
DTSTAMP:20260417T160759
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:20220111T163000
DTEND;TZID=Asia/Seoul:20220111T173000
DTSTAMP:20260417T160759
CREATED:20220111T073000Z
LAST-MODIFIED:20240707T080542Z
UID:5083-1641918600-1641922200@dimag.ibs.re.kr
SUMMARY:Andreas Holmsen\, Some recent results on geometric transversals
DESCRIPTION:A geometric transversal to a family of convex sets in $\mathbb R^d$ is an affine flat that intersects the members of the family. While there exists a far-reaching theory concerning 0-dimensional transversals (intersection patterns of convex sets)\, much less is known when it comes to higher-dimensional transversals. In this talk\, I will present some new and old results and problems regarding geometric transversals\, based on joint work with Otfried Cheong and Xavier Goaoc.
URL:https://dimag.ibs.re.kr/event/2022-01-11/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220104T163000
DTEND;TZID=Asia/Seoul:20220104T173000
DTSTAMP:20260417T160759
CREATED:20211210T230406Z
LAST-MODIFIED:20240707T080549Z
UID:5000-1641313800-1641317400@dimag.ibs.re.kr
SUMMARY:Seunghun Lee (이승훈)\, Transversals and colorings of simplicial spheres
DESCRIPTION:Motivated from the surrounding property of a point set in $\mathbb{R}^d$ introduced by Holmsen\, Pach and Tverberg\, we consider the transversal number and chromatic number of a simplicial sphere. As an attempt to give a lower bound for the maximum transversal ratio of simplicial $d$-spheres\, we provide two infinite constructions. The first construction gives infinitely many $(d+1)$-dimensional simplicial polytopes with the transversal ratio exactly $\frac{2}{d+2}$ for every $d\geq 2$. In the case of $d=2$\, this meets the previously well-known upper bound $1/2$ tightly. The second gives infinitely many simplicial 3-spheres with the transversal ratio greater than $1/2$. This was unexpected from what was previously known about the surrounding property. Moreover\, we show that\, for $d\geq 3$\, the facet hypergraph $\mathcal{F}(\mathbf{P})$ of a $(d+1)$-dimensional simplicial polytope $\mathbf{P}$ has the chromatic number $\chi(\mathcal{F}(\mathbf{P})) \in O(n^{\frac{\lceil d/2\rceil-1}{d}})$\, where $n$ is the number of vertices of $\mathbf{P}$. This slightly improves the upper bound previously obtained by Heise\, Panagiotou\, Pikhurko\, and Taraz. This is a joint work with Joseph Briggs and Michael Gene Dobbins.
URL:https://dimag.ibs.re.kr/event/2022-01-04/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;VALUE=DATE:20211220
DTEND;VALUE=DATE:20211223
DTSTAMP:20260417T160759
CREATED:20211219T150000Z
LAST-MODIFIED:20240707T080557Z
UID:4146-1639958400-1640217599@dimag.ibs.re.kr
SUMMARY:2021 Combinatorics Workshop (2021 조합론 학술대회)
DESCRIPTION:The Combinatorics Workshop (조합론 학술대회) is an annual conference of combinatorialists in Korea that started in 2004 by the Yonsei University BK21 Research Group. Since 2013\, this workshop has been advised by the committee of discrete mathematics of the Korean Mathematical Society. This year it will take place at The Bloomvista in Yangpyeong on December 20-22\, 2021. \nThe aim of this workshop is to bring together active researchers with different backgrounds to discuss recent and prospective advances in combinatorics and related areas. \nWe plan to limit the number of participants. Registration (without a fee) will be required. General participants will be required to pay for their own accommodation. \n\nTitle: 2021 Combinatorics Workshop (2021 조합론 학술대회)\nDate: December 20 – 22 (Mon-Wed)\, 2021\nVenue: The Bloomvista\, Yangpyeong\nWebsite: https://cw2021.combinatorics.kr\n\nPlan\n\nStarting in the afternoon of Thursday and ending in the morning of Wednesday.\nThere will be 5 invited talks for 50 minutes each.\nThere will be contributed talks for 25 minutes each.\n\nUsing English is recommended if there are non-Korean participants in the audience.\nThe call for contributed talks will be announced later.\n\n\nIt will be an offline meeting.\n\nInvited Speakers\n\nDongsu Kim\, KAIST\nJoonkyung Lee\, Hanyang University\nHong Liu\, University of Warwick\, UK\nSuil O\, SUNY Korea\nSeonjeong Park\, Jeonju University\n\nCall for Abstracts\nWe are looking for contributed talks! If you are interested in giving a contributed talk\, then please submit your abstract until November 15\, 2021. \nRegistration\n\nPlease fill out the registration form by November 21\, 2021.\n\nThe registration is free.\nThe organizers will announce the price for the accommodation soon.\n\n\nDue to the government COVID-19 policy\, the organizers may reject some registration\, even if the registration was made before November 21.\n\nOrganizing Committee\n\nJeong-Ok Choi\, GIST\nSang-il Oum\, IBS Discrete Mathematics Group and KAIST\nHeesung Shin\, Inha University\n\nAdvisory Committee\nCommittee of Discrete Mathematics\, The Korean Mathematical Society (Chair: Soojin Cho\, Ajou University) \nHost and Sponsors\nIBS Discrete Mathematics Group
URL:https://dimag.ibs.re.kr/event/2021-combinatorics-workshop/
LOCATION:The Bloomvista
CATEGORIES:Workshops and Conferences
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211214T163000
DTEND;TZID=Asia/Seoul:20211214T173000
DTSTAMP:20260417T160759
CREATED:20211214T073000Z
LAST-MODIFIED:20240705T180035Z
UID:4913-1639499400-1639503000@dimag.ibs.re.kr
SUMMARY:Tuan Tran\, Exponential decay of intersection volume with applications on list-decodability and sphere-covering bounds
DESCRIPTION:We give some natural sufficient conditions for balls in a metric space to have small intersection. Roughly speaking\, this happens when the metric space is (i) expanding and (ii) well-spread\, and (iii) certain random variable on the boundary of a ball has a small tail. As applications\, we show that the volume of intersection of balls in Hamming space and symmetric groups decays exponentially as their centers drift apart. To verify condition (iii)\, we prove some deviation inequalities `on the slice’ for functions with Lipschitz conditions. \nWe then use these estimates on intersection volumes to \n\nobtain a sharp lower bound on list-decodability of random q-ary codes\, confirming a conjecture of Li and Wootters [IEEE Trans. Inf. Theory 2021]; and\nimprove sphere-covering bound from the 70s on constant weight codes by a factor linear in dimension\, resolving a problem raised by Jiang and Vardy [IEEE Trans. Inf. Theory 2004].\n\nOur probabilistic point of view also offers a unified framework to obtain improvements on other sphere-covering bounds\, giving conceptually simple and calculation-free proofs for q-ary codes\, permutation codes\, and spherical codes. \nThis is joint work with Jaehoon Kim and Hong Liu.
URL:https://dimag.ibs.re.kr/event/2021-12-14/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211209T163000
DTEND;TZID=Asia/Seoul:20211209T173000
DTSTAMP:20260417T160759
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:20211207T163000
DTEND;TZID=Asia/Seoul:20211207T173000
DTSTAMP:20260417T160759
CREATED:20211207T073000Z
LAST-MODIFIED:20240707T080616Z
UID:4804-1638894600-1638898200@dimag.ibs.re.kr
SUMMARY:Eun-Kyung Cho (조은경)\, Independent domination of graphs with bounded maximum degree
DESCRIPTION:The independent domination number of a graph $G$\, denoted $i(G)$\, is the minimum size of an independent dominating set of $G$. In this talk\, we prove a series of results regarding independent domination of graphs with bounded maximum degree. \nLet $G$ be a graph with maximum degree at most $k$ where $k \ge 1$. We prove that if $k = 4$\, then $i(G) \le \frac{5}{9}|V(G)|$\, which is tight. Generalizing this result and a result by Akbari et al.\, we suggest a conjecture on the upper bound of $i(G)$ for $k \ge 1$\, which is tight if true. \nLet $G’$ be a connected $k$-regular graph that is not $K_{k\, k}$ where $k\geq 3$. We prove that $i(G’)\le \frac{k-1}{2k-1}|V(G’)|$\, which is tight for $k \in \{3\, 4\}$\, generalizing a result by Lam\, Shiu\, and Sun. This result also answers a question by Goddard et al. in the affirmative. \nIn addition\, we show that $\frac{i(G’)}{\gamma(G’)} \le \frac{k^3-3k^2+2}{2k^2-6k+2}$\, strengthening upon a result of Knor\, Škrekovski\, and Tepeh\, where $\gamma(G’)$ is the domination number of $G’$. \nMoreover\, if we restrict $G’$ to be a cubic graph without $4$-cycles\, then we prove that $i(G’) \le \frac{4}{11}|V(G’)|$\, which improves a result by Abrishami and Henning. \nThis talk is based on joint work with Ilkyoo Choi\, Hyemin Kwon\, and Boram Park.
URL:https://dimag.ibs.re.kr/event/2021-12-07/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211130T163000
DTEND;TZID=Asia/Seoul:20211130T173000
DTSTAMP:20260417T160759
CREATED:20211130T073000Z
LAST-MODIFIED:20240707T080630Z
UID:4852-1638289800-1638293400@dimag.ibs.re.kr
SUMMARY:Seonghyuk Im (임성혁)\, Large clique subdivisions in graphs without small dense subgraphs
DESCRIPTION:What is the largest number $f(d)$ where every graph with average degree at least $d$ contains a subdivision of $K_{f(d)}$? Mader asked this question in 1967 and $f(d) = \Theta(\sqrt{d})$ was proved by Bollobás and Thomason and independently by Komlós and Szemerédi. This is best possible by considering a disjoint union of $K_{d\,d}$. However\, this example contains a much smaller subgraph with the almost same average degree\, for example\, one copy of $K_{d\,d}$. \nIn 2017\, Liu and Montgomery proposed the study on the parameter $c_{\varepsilon}(G)$ which is the order of the smallest subgraph of $G$ with average degree at least $\varepsilon d(G)$. In fact\, they conjectured that for small enough $\varepsilon>0$\, every graph $G$ of average degree $d$ contains a clique subdivision of size $\Omega(\min\{d\, \sqrt{\frac{c_{\varepsilon}(G)}{\log c_{\varepsilon}(G)}}\})$. We prove that this conjecture holds up to a multiplicative $\min\{(\log\log d)^6\,(\log \log c_{\varepsilon}(G))^6\}$-term. \nAs a corollary\, for every graph $F$\, we determine the minimum size of the largest clique subdivision in $F$-free graphs with average degree $d$ up to multiplicative polylog$(d)$-term. \nThis is joint work with Jaehoon Kim\, Youngjin Kim\, and Hong Liu.
URL:https://dimag.ibs.re.kr/event/2021-11-30/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211125T163000
DTEND;TZID=Asia/Seoul:20211125T173000
DTSTAMP:20260417T160759
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:20211123T163000
DTEND;TZID=Asia/Seoul:20211123T173000
DTSTAMP:20260417T160759
CREATED:20211123T073000Z
LAST-MODIFIED:20240707T080759Z
UID:4798-1637685000-1637688600@dimag.ibs.re.kr
SUMMARY:Casey Tompkins\, Ramsey numbers of Boolean lattices
DESCRIPTION:The poset Ramsey number $R(Q_{m}\,Q_{n})$ is the smallest integer $N$ such that any blue-red coloring of the elements of the Boolean lattice $Q_{N}$ has a blue induced copy of $Q_{m}$ or a red induced copy of $Q_{n}$. Axenovich and Walzer showed that $n+2\le R(Q_{2}\,Q_{n})\le2n+2$. Recently\, Lu and Thompson\nimproved the upper bound to $\frac{5}{3}n+2$. In this paper\, we solve this problem asymptotically by showing that $R(Q_{2}\,Q_{n})=n+O(n/\log n)$.\nJoint work with Dániel Grósz and Abhishek Methuku.
URL:https://dimag.ibs.re.kr/event/2021-11-23/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;VALUE=DATE:20211123
DTEND;VALUE=DATE:20211127
DTSTAMP:20260417T160759
CREATED:20211122T150000Z
LAST-MODIFIED:20240705T181013Z
UID:4872-1637625600-1637971199@dimag.ibs.re.kr
SUMMARY:Graph Product Structure Theory: Gathering of Participants from Korea
DESCRIPTION:On November 22-26\, 2021\, there is a “Graph Product Structure Theory” workshop in BIRS Centre in Banff (https://www.birs.ca/events/2021/5-day-workshops/21w5235)\, organized in a hybrid manner with 15 onsite participants and around 50 remote participants. We would like to meet in a group of 5-10 remote participants from Korea in one place\, creating a secondary workshop site in Korea. This would allow joint participation in online talks and in-person discussions between local participants.
URL:https://dimag.ibs.re.kr/event/2021-11-22/
LOCATION:Room B223\, IBS (기초과학연구원)
CATEGORIES:Workshops and Conferences
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211111T163000
DTEND;TZID=Asia/Seoul:20211111T173000
DTSTAMP:20260417T160759
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:20211109T163000
DTEND;TZID=Asia/Seoul:20211109T173000
DTSTAMP:20260417T160759
CREATED:20211109T073000Z
LAST-MODIFIED:20240705T181024Z
UID:4588-1636475400-1636479000@dimag.ibs.re.kr
SUMMARY:Jaehoon Kim (김재훈)\, 2-complexes with unique embeddings in 3-space
DESCRIPTION:A well-known theorem of Whitney states that a 3-connected planar graph admits an essentially unique embedding into the 2-sphere. We prove a 3-dimensional analogue: a simply-connected 2-complex every link graph of which is 3-connected admits an essentially unique locally flat embedding into the 3-sphere\, if it admits one at all. This can be thought of as a generalisation of the 3-dimensional Schoenflies theorem. This is joint work with Agelos Georgakopoulos.
URL:https://dimag.ibs.re.kr/event/2021-11-09/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211105T163000
DTEND;TZID=Asia/Seoul:20211105T173000
DTSTAMP:20260417T160759
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:20211102T163000
DTEND;TZID=Asia/Seoul:20211102T173000
DTSTAMP:20260417T160759
CREATED:20211109T073000Z
LAST-MODIFIED:20240707T080853Z
UID:4780-1635870600-1635874200@dimag.ibs.re.kr
SUMMARY:Ben Lund\, Maximal 3-wise intersecting families
DESCRIPTION:A family $\mathcal F$ of subsets of {1\,2\,…\,n} is called maximal k-wise intersecting if every collection of at most k members from $\mathcal F$ has a common element\, and moreover\, no set can be added to $\mathcal F$ while preserving this property. In 1974\, Erdős and Kleitman asked for the smallest possible size of a maximal k-wise intersecting family\, for k≥3. We resolve this problem for k=3 and n even and sufficiently large. \nThis is joint work with Kevin Hendrey\, Casey Tompkins\, and Tuan Tran.
URL:https://dimag.ibs.re.kr/event/2021-11-02/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211026T163000
DTEND;TZID=Asia/Seoul:20211026T173000
DTSTAMP:20260417T160759
CREATED:20211026T073000Z
LAST-MODIFIED:20240707T080901Z
UID:4709-1635265800-1635269400@dimag.ibs.re.kr
SUMMARY:Donggyu Kim (김동규)\, 𝝘-graphic delta-matroids and their applications
DESCRIPTION:Bouchet (1987) defined delta-matroids by relaxing the base exchange axiom of matroids. Oum (2009) introduced a graphic delta-matroid from a pair of a graph and its vertex subset. We define a $\Gamma$-graphic delta-matroid for an abelian group $\Gamma$\, which generalizes a graphic delta-matroid. \nFor an abelian group $\Gamma$\, a $\Gamma$-labelled graph is a graph whose vertices are labelled by elements of $\Gamma$. We prove that a certain collection of edge sets of a $\Gamma$-labelled graph forms a delta-matroid\, which we call a $\Gamma$-graphic delta-matroid\, and provide a polynomial-time algorithm to solve the separation problem\, which allows us to apply the symmetric greedy algorithm of Bouchet (1987) to find a maximum weight feasible set in such a delta-matroid. We also prove that a $\Gamma$-graphic delta-matroid is a graphic delta-matroid if and only if it is even. We prove that every $\mathbb{Z}_p^k$-graphic delta matroid is represented by some symmetric matrix over a field of characteristic of order $p^k$\, and if every $\Gamma$-graphic delta-matroid is representable over a finite field $\mathbb{F}$\, then $\Gamma$ is isomorphic to $\mathbb{Z}_p^k$ and $\mathbb{F}$ is a field of order $p^\ell$ for some prime $p$ and positive integers $k$ and $\ell$. \nThis is joint work with Duksang Lee and Sang-il Oum.
URL:https://dimag.ibs.re.kr/event/2021-10-26/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;VALUE=DATE:20211020
DTEND;VALUE=DATE:20211023
DTSTAMP:20260417T160759
CREATED:20211019T150000Z
LAST-MODIFIED:20240707T092447Z
UID:4324-1634688000-1634947199@dimag.ibs.re.kr
SUMMARY:Young Researchers in Extremal and Probabilistic Combinatorics
DESCRIPTION:The aim of the Young Researchers in Extremal and Probabilistic Combinatorics is to bring together early career researchers working on these topics.  The workshop will consist of several  25 minute talks across three days from October 20 to 22\, 2021.  Due to Covid the workshop will be held online. \n \nInvited Speakers & Program\nOct. 20 Wednesday 4 PM (KST) – 8 PM (KST)\n\nAndrzej Grzesik (Jagiellonian University): Degenerated generalized Turán numbers of cycles\, 4:00-4:25\nJan Volec (Czech Technical University): Existence of common graphs with large chromatic number\, 4:30-4:55\nBalázs Patkós (Rényi Institute): Vector sum-intersection theorems\, 5:00-5:25\nIstván Tomon (ETH Zurich): Small doubling\, atomic structure and $\ell$-divisible set families\, 5:30-5:55\nMichael Anastos (Freie Universität Berlin): Longest Cycles in Sparse Random Graphs and Where to Find Them\, 6:30-6:55\nAdam Zsolt Wagner (Tel Aviv University): Constructions in combinatorics via neural networks\, 7:00-7:25\nYelena Yuditsky (Université libre de Bruxelles): On multicolor Ramsey numbers and subset-coloring of hypergraphs\, 7:30-7:55\n\nOct. 21 Thursday 4 PM (KST) – 8 PM (KST)\n\nKevin Hendrey (IBS Discrete Mathematics Group): Extremal functions for sparse minors\, 4:00-4:25\nSimona Boyadzhiyska (Freie Universität Berlin): Ramsey simplicity of random graphs\, 4:30-4:55\nShagnik Das (National Taiwan University): Schur’s Theorem in randomly perturbed sets\, 5:00-5:25\nTony Huynh (Monash University): Subgraph densities in minor-closed classes (and beyond)\, 5:30-5:55\nAnder Lamaison (Masaryk University): Hypergraphs with minimum uniform Turán density\, 6:30-6:55\nBen Lund (IBS Discrete Mathematics Group): Maximal 3-wise intersecting families\, 7:00-7:25\nLiana Yepremyan (London School of Economics): Enumerating independent sets in Abelian Cayley graphs\, 7:30-7:55\n\nOct. 22 Friday 4 PM (KST) – 8 PM (KST)\n\nAndrey Kupavskii (CNRS): Binary scalar products\, 4:00-4:25\nDániel Gerbner (Rényi Institute): Exact results for generalized Turán problems\, 4:30-4:55\nOliver Janzer (University of Cambridge): Tiling with monochromatic bipartite graphs of bounded maximum degree\, 5:00-5:25\nNika Salia (Rényi Institute): Pósa-type results for Berge Hypergraphs\, 5:30-5:55\nDebsoumya Chakraborti (IBS Discrete Mathematics Group): Mixing time and expanders\, 6:30-6:55\nWei-Tian Li (National Chung Hsing University): Ramsey Properties for $V$-shaped Posets in the Boolean Lattices\, 7:00-7:25\nDimitry Zakharov (Moscow Institute of Physics and Technology): Zero subsums in vector spaces over finite fields\, 7:30-7:55\n\nAbstracts (pdf file) \n 
URL:https://dimag.ibs.re.kr/event/2021-10-20/
LOCATION:Zoom ID: 554 788 7710 (507464)
CATEGORIES:Workshops and Conferences
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211012T163000
DTEND;TZID=Asia/Seoul:20211012T173000
DTSTAMP:20260417T160759
CREATED:20211012T073000Z
LAST-MODIFIED:20240707T080915Z
UID:4374-1634056200-1634059800@dimag.ibs.re.kr
SUMMARY:Joonkyung Lee (이준경)\, Majority dynamics on sparse random graphs
DESCRIPTION:Majority dynamics on a graph $G$ is a deterministic process such that every vertex updates its $\pm 1$-assignment according to the majority assignment on its neighbor simultaneously at each step. Benjamini\, Chan\, O’Donnell\, Tamuz and Tan conjectured that\, in the Erdős-Rényi random graph $G(n\,p)$\, the random initial $\pm 1$-assignment converges to a $99\%$-agreement with high probability whenever $p=\omega(1/n)$. \nThis conjecture was first confirmed for $p\geq\lambda n^{-1/2}$ for a large constant $\lambda$ by Fountoulakis\, Kang and Makai. Although this result has been reproved recently by Tran and Vu and by Berkowitz and Devlin\, it was unknown whether the conjecture holds for $p< \lambda n^{-1/2}$. We break this $\Omega(n^{-1/2})$-barrier by proving the conjecture for sparser random graphs $G(n\,p)$\, where $\lambda’ n^{-3/5}\log n \leq p \leq \lambda n^{-1/2}$ with a large constant $\lambda’>0$. \nJoint work with Debsoumya Chakraborti\, Jeong Han Kim and Tuan Tran.
URL:https://dimag.ibs.re.kr/event/2021-10-12/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211008T100000
DTEND;TZID=Asia/Seoul:20211008T110000
DTSTAMP:20260417T160759
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:20211005T163000
DTEND;TZID=Asia/Seoul:20211005T173000
DTSTAMP:20260417T160759
CREATED:20211005T073000Z
LAST-MODIFIED:20240707T080940Z
UID:4503-1633451400-1633455000@dimag.ibs.re.kr
SUMMARY:Eunjin Oh (오은진)\, Feedback Vertex Set on Geometric Intersection Graphs
DESCRIPTION:I am going to present an algorithm for computing a feedback vertex set of a unit disk graph of size k\, if it exists\, which runs in time $2^{O(\sqrt{k})}(n + m)$\, where $n$ and $m$ denote the numbers of vertices and edges\, respectively. This improves the $2^{O(\sqrt{k}\log k)}(n + m)$-time algorithm for this problem on unit disk graphs by Fomin et al. [ICALP 2017].
URL:https://dimag.ibs.re.kr/event/2021-10-05/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210930T163000
DTEND;TZID=Asia/Seoul:20210930T173000
DTSTAMP:20260417T160759
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:20210928T163000
DTEND;TZID=Asia/Seoul:20210928T173000
DTSTAMP:20260417T160759
CREATED:20210928T073000Z
LAST-MODIFIED:20240707T080955Z
UID:4452-1632846600-1632850200@dimag.ibs.re.kr
SUMMARY:Kevin Hendrey\, Extremal functions for sparse minors
DESCRIPTION:The extremal function $c(H)$ of a graph $H$ is the supremum of densities of graphs not containing $H$ as a minor\, where the density of a graph is the ratio of the number of edges to the number of vertices. Myers and Thomason (2005)\, Norin\, Reed\, Thomason and Wood (2020)\, and Thomason and Wales (2019) determined the asymptotic behaviour of $c(H)$ for all polynomially dense graphs $H$\, as well as almost all graphs of constant density. We explore the asymptotic behavior of the extremal function in the regime not covered by the above results\, where in addition to having constant density the graph $H$ is in a graph class admitting strongly sublinear separators. We establish asymptotically tight bounds in many cases. For example\, we prove that for every planar graph $H$\, \[c(H) = (1+o(1))\max (v(H)/2\, v(H)-\alpha(H))\,\] extending recent results of Haslegrave\, Kim and Liu (2020). Joint work with Sergey Norin and David R. Wood.
URL:https://dimag.ibs.re.kr/event/2021-09-28/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210907T163000
DTEND;TZID=Asia/Seoul:20210907T173000
DTSTAMP:20260417T160759
CREATED:20210907T073000Z
LAST-MODIFIED:20240705T182054Z
UID:4495-1631032200-1631035800@dimag.ibs.re.kr
SUMMARY:Dabeen Lee (이다빈)\, Mixing sets\, submodularity\, and chance-constrained optimization
DESCRIPTION:A particularly important substructure in modeling joint linear chance-constrained programs with random right-hand sides and finite sample space is the intersection of mixing sets with common binary variables (and possibly a knapsack constraint). In this talk\, we first explain basic mixing sets by establishing a strong and previously unrecognized connection to submodularity. In particular\, we show that mixing inequalities with binary variables are nothing but the polymatroid inequalities associated with a specific submodular function. This submodularity viewpoint enables us to unify and extend existing results on valid inequalities and convex hulls of the intersection of multiple mixing sets with common binary variables. Then\, we study such intersections under an additional linking constraint lower bounding a linear function of the continuous variables. This is motivated from the desire to exploit the information encoded in the knapsack constraint arising in joint linear CCPs via the quantile cuts. We propose a new class of valid inequalities and characterize when this new class along with the mixing inequalities are sufficient to describe the convex hull. This is based on joint work with Fatma Fatma Kılınç-Karzan and Simge Küçükyavuz.
URL:https://dimag.ibs.re.kr/event/2021-09-07/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210831T163000
DTEND;TZID=Asia/Seoul:20210831T173000
DTSTAMP:20260417T160759
CREATED:20210831T073000Z
LAST-MODIFIED:20240707T081024Z
UID:4341-1630427400-1630431000@dimag.ibs.re.kr
SUMMARY:Cheolwon Heo (허철원)\, Representations of even-cycle matroids
DESCRIPTION:A signed graph is a pair $(G\,\Sigma)$ where $G$ is a graph and $\Sigma$ is a subset of edges of $G$. A cycle $C$ of $G$ is a subset of edges of $G$ such that every vertex of the subgraph of $G$ induced by $C$ has an even degree. We say that $C$ is even in $(G\,\Sigma)$ if $|C \cap \Sigma|$ is even; otherwise\, $C$ is odd. A matroid $M$ is an even-cycle matroid if there exists a signed graph $(G\,\Sigma)$ such that circuits of $M$ precisely corresponds to inclusion-wise minimal non-empty even cycles of $(G\,\Sigma)$. For even-cycle matroids\, two fundamental questions arise:\n(1) what is the relationship between two signed graphs representing the same even-cycle matroids?\n(2) how many signed graphs can an even-cycle matroid have?\nFor (a)\, we characterize two signed graphs $(G_1\,\Sigma_1)$ and $(G_2\,\Sigma_2)$ where $G_1$ and $G_2$ are $4$-connected that represent the same even-cycle matroids.\nFor (b)\, we introduce pinch-graphic matroids\, which can generate exponentially many representations even when the matroid is $3$-connected. An even-cycle matroid is a pinch-graphic matroid if there exists a signed graph with a pair of vertices such that every odd cycle intersects with at least one of them. We prove that there exists a constant $c$ such that if a matroid is even-cycle matroid that is not pinch-graphic\, then the number of representations is bounded by $c$. This is joint work with Bertrand Guenin and Irene Pivotto.
URL:https://dimag.ibs.re.kr/event/2021-08-31/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210824T163000
DTEND;TZID=Asia/Seoul:20210824T173000
DTSTAMP:20260417T160759
CREATED:20210810T073000Z
LAST-MODIFIED:20240707T081032Z
UID:4212-1629822600-1629826200@dimag.ibs.re.kr
SUMMARY:Eun Jung Kim (김은정)\, A Constant-factor Approximation for Weighted Bond Cover
DESCRIPTION:The Weighted $\mathcal F$-Vertex Deletion for a class $\mathcal F$ of graphs asks\, given a weighted graph $G$\, for a minimum weight vertex set $S$ such that $G-S\in\mathcal F$. The case when $\mathcal F$ is minor-closed and excludes some graph as a minor has received particular attention but a constant-factor approximation remained elusive for Weighted $\mathcal F$-Vertex Deletion. Only three cases of minor-closed $\mathcal F$ are known to admit constant-factor approximations\, namely Vertex Cover\, Feedback Vertex Set and Diamond Hitting Set. \nWe study the problem for the class $\mathcal F$ of $\theta_c$-minor-free graphs\, under the equivalent setting of the Weighted c-Bond Cover\, and present a constant-factor approximation algorithm using the primal-dual method. For this\, we leverage a structure theorem implicit in [Joret et al.\, SIDMA’14] which states the following: any graph $G$ containing a $\theta_c$-minor-model either contains a large two-terminal protrusion\, or contains a constant-size $\theta_c$-minor-model\, or a collection of pairwise disjoint constant-sized connected sets that can be contracted simultaneously to yield a dense graph. In the first case\, we tame the graph by replacing the protrusion with a special-purpose weighted gadget. For the second and third case\, we provide a weighting scheme which guarantees a local approximation ratio. Besides making an important step in the quest of (dis)proving a constant-factor approximation for Weighted $\mathcal F$-Vertex Deletion\, our result may be useful as a template for algorithms for other minor-closed families. \nThis is joint work with Euiwoong Lee and Dimitrios M. Thilikos.
URL:https://dimag.ibs.re.kr/event/2021-08-24/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210818T170000
DTEND;TZID=Asia/Seoul:20210818T180000
DTSTAMP:20260417T160759
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:20210817T163000
DTEND;TZID=Asia/Seoul:20210817T173000
DTSTAMP:20260417T160759
CREATED:20210817T073000Z
LAST-MODIFIED:20240707T081153Z
UID:4242-1629217800-1629221400@dimag.ibs.re.kr
SUMMARY:Linda Cook\, Two results on graphs with holes of restricted lengths
DESCRIPTION:We call an induced cycle of length at least four a hole. The parity of a hole is the parity of its length. Forbidding holes of certain types in a graph has deep structural implications. In 2006\, Chudnovksy\, Seymour\, Robertson\, and Thomas famously proved that a graph is perfect if and only if it does not contain an odd hole or a complement of an odd hole. In 2002\, Conforti\, Cornuéjols\, Kapoor\, and Vuškovíc provided a structural description of the class of even-hole-free graphs. I will describe the structure of all graphs that contain only holes of length $\ell$ for every $\ell \geq 7$ (joint work with Jake Horsfield\, Myriam Preissmann\, Paul Seymour\, Ni Luh Dewi Sintiari\, Cléophée Robin\, Nicolas Trotignon\, and Kristina Vuškovíc. \nAnalysis of how holes interact with graph structure has yielded detection algorithms for holes of various lengths and parities. In 1991\, Bienstock showed it is NP-Hard to test whether a graph G has an even (or odd) hole containing a specified vertex $v \in V(G)$. In 2002\, Conforti\, Cornuéjols\, Kapoor\, and Vuškovíc gave a polynomial-time algorithm to recognize even-hole-free graphs using their structure theorem. In 2003\, Chudnovsky\, Kawarabayashi\, and Seymour provided a simpler and slightly faster algorithm to test whether a graph contains an even hole. In 2019\, Chudnovsky\, Scott\, Seymour\, and Spirkl provided a polynomial-time algorithm to test whether a graph contains an odd hole. Later that year\, Chudnovsky\, Scott\, and Seymour strengthened this result by providing a polynomial-time algorithm to test whether a graph contains an odd hole of length at least $\ell$ for any fixed integer $\ell \geq 5$. I will present a polynomial-time algorithm (joint work with Paul Seymour) to test whether a graph contains an even hole of length at least $\ell$ for any fixed integer $\ell \geq 4$.
URL:https://dimag.ibs.re.kr/event/2021-08-17/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
END:VCALENDAR