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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:20190101T000000
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END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210302T163000
DTEND;TZID=Asia/Seoul:20210302T173000
DTSTAMP:20260418T050918
CREATED:20210217T044249Z
LAST-MODIFIED:20240707T081721Z
UID:3639-1614702600-1614706200@dimag.ibs.re.kr
SUMMARY:Kevin Hendrey\, A unified half-integral Erdős-Pósa theorem for cycles in graphs labelled by multiple abelian groups
DESCRIPTION:Erdős and Pósa proved in 1965 that there is a duality between the maximum size of a packing of cycles and the minimum size of a vertex set hitting all cycles. Such a duality does not hold if we restrict to odd cycles.  However\, in 1999\, Reed proved an analogue for odd cycles by relaxing packing to half-integral packing. We prove a far-reaching generalisation of the theorem of Reed; if the edges of a graph are labelled by finitely many abelian groups\, then there is a duality between the maximum size of a half-integral packing of cycles whose values avoid a fixed finite set for each abelian group and the minimum size of a vertex set hitting all such cycles. \nA multitude of natural properties of cycles can be encoded in this setting\, for example cycles of length at least $\ell$\, cycles of length $p$ modulo $q$\, cycles intersecting a prescribed set of vertices at least $t$ times\, and cycles contained in given $\mathbb{Z}_2$-homology classes in a graph embedded on a fixed surface. Our main result allows us to prove a duality theorem for cycles satisfying a fixed set of finitely many such properties. \nThis is joint work with J. Pascal Gollin\, Ken-ichi Kawarabayashi\, O-joung Kwon\, and Sang-il Oum.
URL:https://dimag.ibs.re.kr/event/2021-03-02/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210223T163000
DTEND;TZID=Asia/Seoul:20210223T173000
DTSTAMP:20260418T050918
CREATED:20210217T043908Z
LAST-MODIFIED:20240707T081835Z
UID:3637-1614097800-1614101400@dimag.ibs.re.kr
SUMMARY:Minki Kim (김민기)\, Rainbow paths and rainbow matchings
DESCRIPTION:We prove that if $n \geq 3$\, then any family of $3n-3$ sets of matchings of size $n$ in any graph has a rainbow matching of size $n$. This improves on a previous result\, in which $3n-3$ is replaced by $3n-2$. We also prove a “cooperative” generalization: for $t > 0$ and $n \geq 3$\, any $3n-4+t$ sets of edges\, the union of every $t$ of which contains a matching of size $n$\, have rainbow matching of size $n$. This is joint work with Ron Aharoni\, Joseph Briggs\, and Jinha Kim.
URL:https://dimag.ibs.re.kr/event/2021-02-23/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210217T100000
DTEND;TZID=Asia/Seoul:20210217T110000
DTSTAMP:20260418T050918
CREATED:20201231T022333Z
LAST-MODIFIED:20240707T081843Z
UID:3423-1613556000-1613559600@dimag.ibs.re.kr
SUMMARY:David Wood\, Tree densities of sparse graph classes
DESCRIPTION:This talk considers the following question at the intersection of extremal and structural graph theory: What is the maximum number of copies of a fixed forest $T$ in an $n$-vertex graph in a graph class $\mathcal{G}$ as $n\to \infty$? I will answer this question for a variety of sparse graph classes $\mathcal{G}$. In particular\, we show that the answer is $\Theta(n^{\alpha_d(T)})$ where $\alpha_d(T)$ is the size of the largest stable set in the subforest of $T$ induced by the vertices of degree at most $d$\, for some integer $d$ that depends on $\mathcal{G}$. For example\, when $\mathcal{G}$ is the class of $k$-degenerate graphs then $d=k$; when $\mathcal{G}$ is the class of graphs containing no $K_{s\,t}$-minor ($t\geq s$) then $d=s-1$; and when $\mathcal{G}$ is the class of $k$-planar graphs then $d=2$. All these results are in fact consequences of a single lemma in terms of a finite set of excluded subgraphs. This is joint work with Tony Huynh (arXiv:2009.12989).
URL:https://dimag.ibs.re.kr/event/2021-02-17/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210216T163000
DTEND;TZID=Asia/Seoul:20210216T173000
DTSTAMP:20260418T050918
CREATED:20210205T012237Z
LAST-MODIFIED:20240705T191023Z
UID:3594-1613493000-1613496600@dimag.ibs.re.kr
SUMMARY:Martin Ziegler\, Quantitative Coding and Complexity Theory of Continuous Data
DESCRIPTION:Specifying a computational problem requires fixing encodings for input and output: encoding graphs as adjacency matrices\, characters as integers\, integers as bit strings\, and vice versa. For such discrete data\, the actual encoding is usually straightforward and/or complexity-theoretically inessential (up to polynomial time\, say). \nBut concerning continuous data\, already real numbers naturally suggest various encodings with very different computational properties. \nWe recall the existing qualitative theory of computably ‘sensible’ encodings of topological spaces; and we newly develop the quantitative theory of complexity-theoretically ‘sensible’ encodings of metric spaces. \nJoint work with Donghyun Lim.
URL:https://dimag.ibs.re.kr/event/2021-02-16/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210210T163000
DTEND;TZID=Asia/Seoul:20210210T173000
DTSTAMP:20260418T050918
CREATED:20201231T073729Z
LAST-MODIFIED:20240705T191150Z
UID:3428-1612974600-1612978200@dimag.ibs.re.kr
SUMMARY:Jie Ma (马杰)\, Non-repeated cycle lengths and Sidon sequences
DESCRIPTION:We prove a conjecture of Boros\, Caro\, Furedi and Yuster on the maximum number of edges in a 2-connected graph without repeated cycle lengths\, which is a restricted version of a longstanding problem of Erdos. Our proof together with the matched lower bound construction of Boros\, Caro\, Furedi and Yuster show that this problem can be conceptually reduced to the seminal problem of finding the maximum Sidon sequences in number theory. Joint work with Tianchi Yang.
URL:https://dimag.ibs.re.kr/event/2021-02-10/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210209T163000
DTEND;TZID=Asia/Seoul:20210209T173000
DTSTAMP:20260418T050918
CREATED:20210203T050722Z
LAST-MODIFIED:20240705T191023Z
UID:3581-1612888200-1612891800@dimag.ibs.re.kr
SUMMARY:Doowon Koh (고두원)\, On the cone restriction conjecture in four dimensions and applications in incidence geometry
DESCRIPTION:Main purpose of this talk is to introduce a connection between restriction estimates for cones and point-sphere incidence theorems in the finite field setting. First\, we review the finite field restriction problem for cones and address new results on the conical restriction problems. In particular\, we establish the restriction conjecture for the cone in four dimensions. Second\, we study how to apply the conical restriction results to the point-sphere incidence bounds. As a consequence\, we obtain sharp point-sphere incidence bounds when sphere sets are not too big.
URL:https://dimag.ibs.re.kr/event/2021-02-09/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210203T163000
DTEND;TZID=Asia/Seoul:20210203T173000
DTSTAMP:20260418T050918
CREATED:20201106T054235Z
LAST-MODIFIED:20240705T193028Z
UID:3241-1612369800-1612373400@dimag.ibs.re.kr
SUMMARY:Ron Aharoni\, Colorful KKM and multiple cakes division
DESCRIPTION:In the “cake partition” problem n players have each a list of preferred parts for any partition of the [0\,1] interval (“cake”) into n sub-intervals. Woodall\, Stromquist and Gale proved independently that under mild conditions on the list of preferences (like continuity) there is always a partition and assignment of parts to the players\, in which every player gets a piece belonging to her list of preferred parts. In fact\, Gale proved a colorful version of the famous KKM theorem\, not realizing that this is the same problem\, but on the other hand\, proved the problem its proper setting. I will discuss the case of partitioning more than one cake – how many players can you make happy\, when there is a general number of cakes\, and general number of players. \nJoint work with Eli Berger\, Joseph Briggs\, Erel Segal-Halevi and Shira Zerbib.
URL:https://dimag.ibs.re.kr/event/2021-02-03/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210127T100000
DTEND;TZID=Asia/Seoul:20210127T110000
DTSTAMP:20260418T050918
CREATED:20210114T124234Z
LAST-MODIFIED:20240705T191135Z
UID:3500-1611741600-1611745200@dimag.ibs.re.kr
SUMMARY:Dong Yeap Kang (강동엽)\, A proof of the Erdős-Faber-Lovász conjecture
DESCRIPTION:A hypergraph is linear if every pair of two distinct edges shares at most one vertex. A longstanding conjecture by Erdős\, Faber\, and Lovász in 1972\, states that the chromatic index of any linear hypergraph on $n$ vertices is at most $n$. \nIn this talk\, I will present the ideas to prove the conjecture for all large $n$. This is joint work with Tom Kelly\, Daniela Kühn\, Abhishek Methuku\, and Deryk Osthus.
URL:https://dimag.ibs.re.kr/event/2021-01-27/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210126T043000
DTEND;TZID=Asia/Seoul:20210126T173000
DTSTAMP:20260418T050918
CREATED:20210125T042312Z
LAST-MODIFIED:20240707T081932Z
UID:3545-1611635400-1611682200@dimag.ibs.re.kr
SUMMARY:Tuan Tran\, Minimum saturated families of sets
DESCRIPTION:A family $\mathcal F$ of subsets of [n] is called s-saturated if it contains no s pairwise disjoint sets\, and moreover\, no set can be added to $\mathcal F$ while preserving this property. More than 40 years ago\, Erdős and Kleitman conjectured that an s-saturated family of subsets of [n] has size at least $(1 – 2^{-(s-1)})2^n$. It is a simple exercise to show that every s-saturated family has size at least $2^{n-1}$\, but\, as was mentioned by Frankl and Tokushige\, even obtaining a slightly better bound of $(1/2 + \varepsilon)2^n$\, for some fixed $\varepsilon > 0$\, seems difficult. We prove such a result\, showing that every s-saturated family of subsets of [n] has size at least $(1 – 1/s)2^n$. In this talk\,  I will present two short proofs. This is joint work with M. Bucic\, S. Letzter and B. Sudakov.
URL:https://dimag.ibs.re.kr/event/2021-01-26/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210120T163000
DTEND;TZID=Asia/Seoul:20210120T173000
DTSTAMP:20260418T050918
CREATED:20201211T084524Z
LAST-MODIFIED:20240707T081951Z
UID:3358-1611160200-1611163800@dimag.ibs.re.kr
SUMMARY:Yusuke Kobayashi (小林 佑輔)\, An FPT Algorithm for Minimum Additive Spanner Problem
DESCRIPTION:For a positive integer t and a graph G\, an additive t-spanner of G is a spanning subgraph in which the distance between every pair of vertices is at most the original distance plus t. Minimum Additive t-Spanner Problem is to find an additive t-spanner with the minimum number of edges in a given graph\, which is known to be NP-hard. Since we need to care about global properties of graphs when we deal with additive t-spanners\, Minimum Additive t-Spanner Problem is hard to handle\, and hence only few results are known for it. In this talk\, we study Minimum Additive t-Spanner Problem from the viewpoint of parameterized complexity. We formulate a parameterized version of the problem in which the number of removed edges is regarded as a parameter\, and give a fixed-parameter algorithm for it. We also extend our result to (α\,β)-spanners.
URL:https://dimag.ibs.re.kr/event/2021-01-20/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210119T163000
DTEND;TZID=Asia/Seoul:20210119T173000
DTSTAMP:20260418T050918
CREATED:20210114T070412Z
LAST-MODIFIED:20240705T191136Z
UID:3498-1611073800-1611077400@dimag.ibs.re.kr
SUMMARY:Ben Lund\, Perfect matchings and derangements on graphs
DESCRIPTION:We show that each perfect matching in a bipartite graph G intersects at least half of the perfect matchings in G. This result has equivalent formulations in terms of the permanent of the adjacency matrix of a graph\, and in terms of derangements and permutations on graphs. We give several related results and open questions. This is joint work with Matija Bucic\, Pat Devlin\, Mo Hendon\, and Dru Horne.
URL:https://dimag.ibs.re.kr/event/2021-01-19/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210113T100000
DTEND;TZID=Asia/Seoul:20210113T110000
DTSTAMP:20260418T050918
CREATED:20201126T045239Z
LAST-MODIFIED:20240705T192124Z
UID:3318-1610532000-1610535600@dimag.ibs.re.kr
SUMMARY:Rose McCarty\, Vertex-minors and flooding immersions
DESCRIPTION:An immersion of a graph H into a graph G sends edges of H into edge-disjoint trails of G. We say the immersion is flooding if every edge of G is in one of the trails. Flooding immersions are interesting for Eulerian group-labelled graphs; in this context they behave quite differently from regular immersions. Moreover\, understanding such flooding immersions is a vital step towards understanding the structure of graphs with a forbidden vertex-minor. \nI will focus on explaining the connection to vertex-minors\, and on recent progress in this direction from ongoing joint work with Jim Geelen and Paul Wollan.
URL:https://dimag.ibs.re.kr/event/2021-01-13/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210112T163000
DTEND;TZID=Asia/Seoul:20210112T173000
DTSTAMP:20260418T050918
CREATED:20201231T074146Z
LAST-MODIFIED:20240705T191150Z
UID:3431-1610469000-1610472600@dimag.ibs.re.kr
SUMMARY:Andreas Holmsen\, Discrete geometry in convexity spaces
DESCRIPTION:The notion of convexity spaces provides a purely combinatorial framework for certain problems in discrete geometry. In the last ten years\, we have seen some progress on several open problems in the area\, and in this talk\, I will focus on the recent results relating to Tverberg’s theorem and the Alon-Kleitman (p\,q) theorem.
URL:https://dimag.ibs.re.kr/event/2021-01-12/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210105T163000
DTEND;TZID=Asia/Seoul:20210105T173000
DTSTAMP:20260418T050918
CREATED:20201126T024545Z
LAST-MODIFIED:20240707T082022Z
UID:3313-1609864200-1609867800@dimag.ibs.re.kr
SUMMARY:O-joung Kwon (권오정)\, Directed tangles and applications
DESCRIPTION:The canonical tree-decomposition theorem\, proved by Robertson and Seymour in their seminal graph minors series\, turns out to be an extremely valuable tool in structural and algorithmic graph theory. In this paper\, we prove the analogous result for digraphs\, the directed tangle tree-decomposition theorem. More precisely\, we introduce directed tangles and provide a directed tree-decomposition of digraphs $G$ that distinguishes all maximal directed tangles in $G$. Furthermore\, for any integer $k$\, we construct a directed tree-decomposition that distinguishes all directed tangles of order $k$\, for any integer $k$. \nBy relaxing the bound slightly\, we can make the previous result algorithmic: for fixed $k$\, we design a polynomial-time algorithm that finds a directed tree-decomposition distinguishing all directed tangles of order $3k$ separated by some separation of order less than $k$. \nWe provide two direct applications of this tangle tree-decomposition theorem. First\, we show that the family of directed odd cycles has the half-integral Erdős-Pósa property\, that is\, there is a function $f:\mathbb{N}\rightarrow \mathbb{R}$ such that for every digraph $G$ and every integer $k$\, either $G$ contains a family of $k$ directed odd cycles where every vertex of $G$ is contained at most two cycles\, or a vertex subset of size at most $f(k)$ hitting all directed odd cycles. This extends the half-integral Erdős-Pósa property for undirected odd cycles\, shown by Reed [Mangoes and blueberries. Combinatorica 1999]. \nSecond\, for every fixed $k$ we show that there is a polynomial-time algorithm which\, on input $G$\, and source and sink vertices $(s_1\, t_1)\, \dots\, (s_k\, t_k)$\, either finds a family of paths $P_1\, \dots\, P_k$ such that each $P_i$ links $s_i$ to $t_i$ and every vertex of $G$ is contained in at most two paths\, or determines that there is no set of pairwise vertex-disjoint paths each connecting $s_i$  to $t_i$. This result improves previous results (with “two” replaced by “three”)\, and given known hardness results\, our result is best possible in a sense that we cannot hope for fixed parameter tractability or fully vertex-disjoint directed paths. \nThis is joint work with Archontia C. Giannopoulou\, Ken-ichi Kawarabayashi\, Stephan Kreutzer\, and Qiqin Xie.
URL:https://dimag.ibs.re.kr/event/2021-01-05/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20201230T100000
DTEND;TZID=Asia/Seoul:20201230T110000
DTSTAMP:20260418T050918
CREATED:20201220T231608Z
LAST-MODIFIED:20240707T082035Z
UID:3389-1609322400-1609326000@dimag.ibs.re.kr
SUMMARY:Paul Seymour\, The Erdős-Hajnal conjecture is true for excluding a five-cycle
DESCRIPTION:In an n-vertex graph\, there must be a clique or stable set of size at least $C\log n$\, and there are graphs where this bound is attained. But if we look at graphs not containing a fixed graph H as an induced subgraph\, the largest clique or stable set is bigger. \nErdős and Hajnal conjectured in 1977 that for every graph H\, there exists c>0 such that every H-free graph has a clique or stable set of size at least $|G|^c$ (“H-free” means not containing H as an induced subgraph\, and |G| means the number of vertices of G). This is still open\, even for some five-vertex graphs H; and the case that has attracted most attention is when H is a cycle of length five. \nIt is true in that case. We will give a sketch of the proof\, which is via applying a lemma about bipartite graphs\, a variant of a theorem of I. Tomon. \nThis lemma has several other applications to the Erdős-Hajnal conjecture. For instance\, it implies that for every cycle C and forest T\, there exists c>0 such that every graph that is both C-free and T’-free (where T’ is the complement of T) has a clique or stable set of size $|G|^c$. (Until now this was open when C has length five and T is a 5-vertex path.) \nJoint work with Maria Chudnovsky\, Alex Scott and Sophie Spirkl.
URL:https://dimag.ibs.re.kr/event/2020-12-30/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20201222T163000
DTEND;TZID=Asia/Seoul:20201222T173000
DTSTAMP:20260418T050918
CREATED:20201208T060000Z
LAST-MODIFIED:20240705T192115Z
UID:3349-1608654600-1608658200@dimag.ibs.re.kr
SUMMARY:Jinha Kim (김진하)\, On a conjecture by Kalai and Meshulam - the Betti number of the independence complex of ternary graphs
DESCRIPTION:Given a graph G=(V\,E)\, the independence complex of G is the abstract simplicial complex I(G) on V whose faces are the independent sets of G. A graph is ternary if it does not contain an induced cycle of length divisible by three. Kalai and Meshulam conjectured that if G is ternary then the sum of the Betti numbers of I(G) is either 0 or 1. In this talk\, I will introduce a result by Zhang and Wu\, which proves the Kalai-Meshulam conjecture.
URL:https://dimag.ibs.re.kr/event/2020-12-22/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20201217T100000
DTEND;TZID=Asia/Seoul:20201217T110000
DTSTAMP:20260418T050918
CREATED:20201028T010135Z
LAST-MODIFIED:20240707T082135Z
UID:3210-1608199200-1608202800@dimag.ibs.re.kr
SUMMARY:Jaiung Jun (전재웅)\, On the Hopf algebra of multi-complexes
DESCRIPTION:In combinatorics\, Hopf algebras appear naturally when studying various classes of combinatorial objects\, such as graphs\, matroids\, posets or symmetric functions. Given such a class of combinatorial objects\, basic information on these objects regarding assembly and disassembly operations are encoded in the algebraic structure of a Hopf algebra. One then hopes to use algebraic identities of a Hopf algebra to return to combinatorial identities of combinatorial objects of interest. \nIn this talk\, I introduce a general class of combinatorial objects\, which we call multi-complexes\, which simultaneously generalizes graphs\, hypergraphs and simplicial and delta complexes. I also introduce a combinatorial Hopf algebra obtained from multi-complexes. Then\, I describe the structure of the Hopf algebra of multi-complexes by finding an explicit basis of the space of primitives\, which is of combinatorial relevance. If time permits\, I will illustrate some potential applications. \nThis is joint work with Miodrag Iovanov.
URL:https://dimag.ibs.re.kr/event/2020-12-17/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20201209T163000
DTEND;TZID=Asia/Seoul:20201209T173000
DTSTAMP:20260418T050918
CREATED:20201013T135938Z
LAST-MODIFIED:20240705T193042Z
UID:3125-1607531400-1607535000@dimag.ibs.re.kr
SUMMARY:Karl Heuer\, Even Circuits in Oriented Matroids
DESCRIPTION:In this talk I will state a generalisation of the even directed cycle problem\, which asks whether a given digraph contains a directed cycle of even length\, to orientations of regular matroids. Motivated by this problem\, I will define non-even oriented matroids generalising non-even digraphs\, which played a central role in resolving the computational complexity of the even dicycle problem. Then I will present and discuss our two results regarding these notions: \nFirst we shall see that the problem of detecting an even directed circuit in a regular matroid is polynomially equivalent to the recognition of non-even oriented matroids. \nSecond and with the main focus for this talk\, we shall characterise the class of non-even oriented bond matroids in terms of forbidden minors\, which complements an existing characterisation of non-even oriented graphic matroids by Seymour and Thomassen. The second result makes use of a new concept of minors for oriented matroids\, which generalises butterfly minors for digraphs to oriented matroids. \nThe part of this talk regarding the second result will be mostly graph theoretical and does not require much knowledge about Matroid Theory. \nThis talk is about joint work [1] with Raphael Steiner and Sebastian Wiederrecht. \n[1] K. Heuer\, R. Steiner and S. Wiederrecht\, Even Circuits in Oriented Matroids\, arxiv:2010.08988
URL:https://dimag.ibs.re.kr/event/2020-12-09/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20201208T163000
DTEND;TZID=Asia/Seoul:20201208T173000
DTSTAMP:20260418T050918
CREATED:20201120T042705Z
LAST-MODIFIED:20240705T193010Z
UID:3287-1607445000-1607448600@dimag.ibs.re.kr
SUMMARY:Hong Liu (刘鸿)\, A solution to Erdős and Hajnal's odd cycle problem
DESCRIPTION:I will go over the history on the study of the set of cycle lengths of graphs with large average degree or chromatic number\, and discuss recent work with Richard Montgomery on this topic. In particular\, we will see the divergence of harmonic sum of odd cycle lengths in graphs with large chromatic number and the appearance of cycle lengths in very sparse sequences (such as powers of 2). The methods developed in this work allows also us to embed equally divided clique subdivisions\, which was conjectured by Thomassen.
URL:https://dimag.ibs.re.kr/event/2020-12-08/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20201203T163000
DTEND;TZID=Asia/Seoul:20201203T173000
DTSTAMP:20260418T050918
CREATED:20201013T135812Z
LAST-MODIFIED:20240705T194003Z
UID:3122-1607013000-1607016600@dimag.ibs.re.kr
SUMMARY:Deniz Sarikaya\, What means Hamiltonicity for infinite graphs and how to force it via forbidden induced subgraphs
DESCRIPTION:The study of Hamiltonian graphs\, i.e. finite graphs having a cycle that contains all vertices of the graph\, is a central theme of finite graph theory. For infinite graphs such a definition cannot work\, since cycles are finite. We shall debate possible concepts of Hamiltonicity for infinite graphs and eventually follow the topological approach by Diestel and Kühn [2\,3]\, which allows to generalize several results about being a Hamiltonian graph to locally finite graphs\, i.e. graphs where each vertex has finite degree. An infinite cycle of a locally finite connected graph G is defined as a homeomorphic image of the unit circle $S^1$  in the Freudenthal compactification |G| of G. Now we call G Hamiltonian if there is an infinite cycle in |G| containing all vertices of G. For an introduction see [1]. \nWe examine how to force Hamiltonicity via forbidden induced subgraphs and present recent extensions of results for Hamiltonicity in finite claw-free graphs to locally finite ones. The first two results are about claw- and net-free graphs\, claw- and bull-free graphs\, the last also about further graph classes being structurally richer\, where we focus on paws as relevant subgraphs\, but relax the condition of forbidding them as induced subgraphs. \nThe goal of the talk is twofold: (1) We introduce the history of the topological viewpoint and argue that there are some merits to it (2) sketch the proofs for the results mentioned above in some details. \nThis is based on joint work [4\,5] with Karl Heuer. \nBibliography\n[1] R. Diestel (2017) Infinite Graphs. In: Graph Theory. Graduate Texts in Mathematics\, vol 173. Springer\, Berlin\, Heidelberg. https://doi.org/10.1007/978-3-662-53622-3_8 \n[2] R. Diestel and D. Kühn\, On infinite cycles I\, Combinatorica 24 (2004)\, pp. 69-89. \n[3] R. Diestel and D. Kühn\, On infinite cycles II\, Combinatorica 24 (2004)\, pp. 91-116. \n[4] K. Heuer and D. Sarikaya\, Forcing Hamiltonicity in locally finite graphs via forbidden induced subgraphs I: nets and bulls\, arXiv:2006.09160 \n[5] K. Heuer and D. Sarikaya\, Forcing Hamiltonicity in locally finite graphs via forbidden induced subgraphs II: paws\, arXiv:2006.09166
URL:https://dimag.ibs.re.kr/event/2020-12-03/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20201202T170000
DTEND;TZID=Asia/Seoul:20201202T180000
DTSTAMP:20260418T050918
CREATED:20201126T022405Z
LAST-MODIFIED:20240705T192124Z
UID:3309-1606928400-1606932000@dimag.ibs.re.kr
SUMMARY:Joonkyung Lee (이준경)\, On common graphs
DESCRIPTION:A graph $H$ is common if the number of monochromatic copies of $H$ in a 2-edge-colouring of the complete graph $K_n$ is minimised by the random colouring. Burr and Rosta\, extending a famous conjecture by Erdős\, conjectured that every graph is common. The conjectures by Erdős and by Burr and Rosta were disproved by Thomason and by Sidorenko\, respectively\, in the late 1980s. \nDespite its importance\, the full classification of common graphs is still a wide open problem and has not seen much progress since the early 1990s. In this lecture\, I will present some old and new techniques to prove whether a graph is common or not.
URL:https://dimag.ibs.re.kr/event/2020-12-02/
LOCATION:Zoom ID:8628398170 (123450)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20201201T163000
DTEND;TZID=Asia/Seoul:20201201T173000
DTSTAMP:20260418T050918
CREATED:20201115T235924Z
LAST-MODIFIED:20240705T193016Z
UID:3273-1606840200-1606843800@dimag.ibs.re.kr
SUMMARY:Debsoumya Chakraborti\, Rainbow matchings in edge-colored simple graphs
DESCRIPTION:There has been much research on finding a large rainbow matching in a properly edge-colored graph\, where a proper edge coloring is a coloring of the edge set such that no same-colored edges are incident. Barát\, Gyárfás\, and Sárközy conjectured that in every proper edge coloring of a multigraph (with parallel edges allowed\, but not loops) with $2q$ colors where each color appears at least $q$ times\, there is always a rainbow matching of size $q$. We prove that $2q + o(q)$ colors are enough if the graph is simple\, confirming the conjecture asymptotically for simple graphs. We also make progress in the lower bound on the required number of colors for simple graphs\, which disproves a conjecture of Aharoni and Berger. We use a randomized algorithm to obtain a large rainbow matching\, and the analysis of the algorithm is based on differential equations method. We will also briefly comment on the limitations of using our probabilistic approach for the problem. This talk will be based on a joint work with Po-Shen Loh.
URL:https://dimag.ibs.re.kr/event/2020-12-01/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20201130T170000
DTEND;TZID=Asia/Seoul:20201130T180000
DTSTAMP:20260418T050918
CREATED:20201126T022202Z
LAST-MODIFIED:20240707T082346Z
UID:3307-1606755600-1606759200@dimag.ibs.re.kr
SUMMARY:Joonkyung Lee (이준경)\, On Ramsey multiplicity
DESCRIPTION:Ramsey’s theorem states that\, for a fixed graph $H$\, every 2-edge-colouring of $K_n$ contains a monochromatic copy of $H$ whenever $n$ is large enough. Perhaps one of the most natural questions after Ramsey’s theorem is then how many copies of monochromatic $H$ can be guaranteed to exist. To formalise this question\, let the Ramsey multiplicity $M(H;n)$ be the minimum number of labelled copies of monochromatic $H$ over all 2-edge-colouring of $K_n$. We define the Ramsey multiplicity constant $C(H)$ is defined by $C(H):=\lim_{n\rightarrow\infty}\frac{M(H\,n)}{n(n-1)\cdots(n-v+1)}$. I will discuss various bounds for C(H) that are known so far.
URL:https://dimag.ibs.re.kr/event/2020-11-30/
LOCATION:Zoom ID:8628398170 (123450)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20201126T100000
DTEND;TZID=Asia/Seoul:20201126T110000
DTSTAMP:20260418T050918
CREATED:20201027T002159Z
LAST-MODIFIED:20240705T193041Z
UID:3195-1606384800-1606388400@dimag.ibs.re.kr
SUMMARY:Da Qi Chen\, Bipartite Saturation
DESCRIPTION:In extremal graph theory\, a graph G is H-saturated if G does not contain a copy of H but adding any missing edge to G creates a copy of H. The saturation number\, sat(n\, H)\, is the minimum number of edges in an n-vertex H-saturated graph. This class of problems was first studied by Zykov and Erdős\, Hajnal\, and Moon. They also determined the saturation number when H is a clique and classified the extremal structures. \nIn this talk\, we will focus mainly on the bipartite saturation problem (which was also first introduced by Erdős\, Hajnal\, and Moon). Here\, we always assume that both G and H are bipartite graphs. Then\, G is H-saturated if G does not contain H but adding any missing edge across the bipartition creates a copy of H. We can then similarly define sat(n\, H) as the minimum number of edges of an n-by-n bipartite graph that is also H-saturated. One of the most interesting and natural questions here is to determine the saturation number for the complete bipartite graph $K_{s\, t}$. When s=t\, the saturation number and its extremal structures were determined long ago but nothing else is known for the general case. Half a decade ago\, Gan\, Korandi\, and Sudakov gave an asymptotically tight bound that was only off by an additive constant.  We will highlight the main ideas behind that proof and show\, with some additional techniques\, how the bound can be improved to achieve tightness for the case when s=t-1. \nThis talk is based on collaborative work with Debsoumya Chakraborti and Mihir Hasabnis. See arXiv: https://arxiv.org/abs/2009.07651 for the full paper.
URL:https://dimag.ibs.re.kr/event/2020-11-26/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20201124T163000
DTEND;TZID=Asia/Seoul:20201124T173000
DTSTAMP:20260418T050918
CREATED:20201111T070608Z
LAST-MODIFIED:20240705T193020Z
UID:3264-1606235400-1606239000@dimag.ibs.re.kr
SUMMARY:Duksang Lee (이덕상)\, Characterizing matroids whose bases form graphic delta-matroids
DESCRIPTION:We introduce delta-graphic matroids\, which are matroids whose bases form graphic delta-matroids. The class of delta-graphic matroids contains graphic matroids as well as cographic matroids and is a proper subclass of the class of regular matroids. We give a structural characterization of the class of delta-graphic matroids. We also show that every forbidden minor for the class of delta-graphic matroids has at most 48 elements. This is joint work with Sang-il Oum.
URL:https://dimag.ibs.re.kr/event/2020-11-24/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20201119T163000
DTEND;TZID=Asia/Seoul:20201119T173000
DTSTAMP:20260418T050918
CREATED:20200927T025647Z
LAST-MODIFIED:20240705T194022Z
UID:3062-1605803400-1605807000@dimag.ibs.re.kr
SUMMARY:Yijia Chen (陈翌佳)\, Graphs of bounded shrub-depth\, through a logic lens
DESCRIPTION:Shrub-depth is a graph invariant often considered as an extension\nof tree-depth to dense graphs. In this talk I will explain our recent\nproofs of two results about graphs of bounded shrub-depth. \n\nEvery graph property definable in monadic-second order logic\,\ne.g.\, 3-colorability\, can be evaluated by Boolean circuits of constant\ndepth and polynomial size\, whose depth only depends on the\nshrub-depth of input graphs.\nGraphs of bounded shrub-depth can be characterized by\na finite set of forbidden induced subgraphs [Ganian et al. 2015].\n\nCentral to the first result is the definability in first-order logic of\ntree-models for graphs of bounded shrub-depth. For the second\nresult\, we observe that shrub-depth can be easily generalized\nto infinite graphs\, and thus some classical tools\, i.e.\, Craig’s\nInterpolation and Łoś-Tarski Theorem\, in model theory are\napplicable to graphs of bounded shrub-depth. \nThis is joint work with Jörg Flum.
URL:https://dimag.ibs.re.kr/event/2020-11-19/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20201111T163000
DTEND;TZID=Asia/Seoul:20201111T173000
DTSTAMP:20260418T050918
CREATED:20200927T024800Z
LAST-MODIFIED:20240707T082419Z
UID:3059-1605112200-1605115800@dimag.ibs.re.kr
SUMMARY:Meike Hatzel\, Constant congestion bramble
DESCRIPTION:In this talk I will present a small result we achieved during a workshop in February this year. My coauthors on this are Marcin Pilipczuk\, Paweł Komosa and Manuel Sorge. \nA bramble in an undirected graph $G$ is a family of connected subgraphs of $G$ such that for every two subgraphs $H_1$ and $H_2$ in the bramble either $V(H_1) \cap V(H_2) \neq \emptyset$ or there is an edge of $G$ with one endpoint in $V(H_1)$ and the second endpoint in $V(H_2)$. The order of the bramble is the minimum size of a vertex set that intersects all elements of a bramble. \nBrambles are objects dual to treewidth: As shown by Seymour and Thomas\, the maximum order of a bramble in an undirected graph $G$ equals one plus the treewidth of $G$. However\, as shown by Grohe and Marx\, brambles of high order may necessarily be of exponential size: In a constant-degree $n$-vertex expander a bramble of order $\Omega(n^{1/2+\delta})$ requires size exponential in $\Omega(n^{2\delta})$ for any fixed $\delta \in (0\,\frac{1}{2}]$. On the other hand\, the combination of results of Grohe and Marx\, and Chekuri and Chuzhoy shows that a graph of treewidth $k$ admits a bramble of order $\widetilde{\Omega}(k^{1/2})$ and size $\widetilde{O}(k^{3/2})$. ($\widetilde{\Omega}$ and $\widetilde{O}$ hide polylogarithmic factors and divisors\, respectively.) \nWe first sharpen the second bound by proving that every graph $G$ of treewidth at least $k$ contains a bramble of order $\widetilde{\Omega}(k^{1/2})$ and congestion $2$\, i.e.\, every vertex of $G$ is contained in at most two elements of the bramble (thus the bramble is of size linear in its order). Second\, we provide a tight upper bound for the lower bound of Grohe and Marx: For every $\delta \in (0\,\frac{1}{2}]$\, every graph $G$ of treewidth at least $k$ contains a bramble of order $\widetilde{\Omega}(k^{1/2+\delta})$ and size $2^{\widetilde{O}(k^{2\delta})}$.
URL:https://dimag.ibs.re.kr/event/2020-11-11/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20201110T163000
DTEND;TZID=Asia/Seoul:20201110T173000
DTSTAMP:20260418T050918
CREATED:20201028T010325Z
LAST-MODIFIED:20240705T193037Z
UID:3212-1605025800-1605029400@dimag.ibs.re.kr
SUMMARY:Casey Tompkins\, Extremal forbidden poset problems in Boolean and linear lattices
DESCRIPTION:Extending the classical theorem of Sperner on the maximum size of an antichain in the Boolean lattice\, Katona and Tarján introduced a general extremal function $La(n\,P)$\, defined to be the maximum size of a family of subsets of $[n]$ which does not contain a given poset $P$ among its containment relations.  In this talk\, I will discuss what is known about the behavior of $La(n\,P)$ and its natural extension to the lattice of subspaces of a vector space over a finite field.  In particular\, I will highlight some recent joint work with Jimeng Xiao.  Many open problems will also be discussed.
URL:https://dimag.ibs.re.kr/event/2020-11-10/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20201105T100000
DTEND;TZID=Asia/Seoul:20201105T110000
DTSTAMP:20260418T050918
CREATED:20200818T142112Z
LAST-MODIFIED:20240707T082448Z
UID:2820-1604570400-1604574000@dimag.ibs.re.kr
SUMMARY:Daniel Cranston\, Vertex Partitions into an Independent Set and a Forest with Each Component Small
DESCRIPTION:For each integer $k\ge 2$\, we determine a sharp bound on\n$\operatorname{mad}(G)$ such that $V(G)$ can be partitioned into sets $I$ and $F_k$\, where $I$ is an independent set and $G[F_k]$ is a forest in which each component has at most k vertices. For each $k$ we construct an infinite family of examples showing our result is best possible. Hendrey\, Norin\, and Wood asked for the largest function $g(a\,b)$ such that if $\operatorname{mad}(G) < g(a\,b)$ then $V(G)$ has a partition into sets $A$ and $B$ such that $\operatorname{mad}(G[A]) < a$ and $\operatorname{mad}(G[B]) < b$. They specifically asked for the value of $g(1\,b)$\, which corresponds to the case that $A$ is an independent set. Previously\, the only values known were $g(1\,4/3)$ and $g(1\,2)$. We find the value of $g(1\,b)$ whenever $4/3 < b < 2$. This is joint work with Matthew Yancey.
URL:https://dimag.ibs.re.kr/event/2020-11-05/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20201103T163000
DTEND;TZID=Asia/Seoul:20201103T173000
DTSTAMP:20260418T050918
CREATED:20201022T132652Z
LAST-MODIFIED:20240705T193042Z
UID:3188-1604421000-1604424600@dimag.ibs.re.kr
SUMMARY:Jaeseong Oh (오재성)\, A 2-isomorphism theorem for delta-matroids
DESCRIPTION:Whitney’s 2-Isomorphism Theorem characterises when two graphs have isomorphic cycle matroids. In this talk\, we present an analogue of this theorem for graphs embedded in surfaces by characterising when two graphs in surface have isomorphic delta-matroids. This is based on the joint work with Iain Moffatt.
URL:https://dimag.ibs.re.kr/event/2020-11-03/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
END:VCALENDAR