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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
REFRESH-INTERVAL;VALUE=DURATION:PT1H
X-Robots-Tag:noindex
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BEGIN:VTIMEZONE
TZID:Asia/Seoul
BEGIN:STANDARD
TZOFFSETFROM:+0900
TZOFFSETTO:+0900
TZNAME:KST
DTSTART:20230101T000000
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20241029T163000
DTEND;TZID=Asia/Seoul:20241029T173000
DTSTAMP:20260416T073418
CREATED:20240919T043705Z
LAST-MODIFIED:20240919T043705Z
UID:9894-1730219400-1730223000@dimag.ibs.re.kr
SUMMARY:Felix Christian Clemen\, Triangles in the Plane
DESCRIPTION:A classical problem in combinatorial geometry\, posed by Erdős in 1946\, asks to determine the maximum number of unit segments in a set of $n$ points in the plane. Since then a great variety of extremal problems in finite planar point sets have been studied. Here\, we look at such questions concerning triangles. Among others we answer the following question asked by Erdős and Purdy almost 50 years ago: Given $n$ points in the plane\, how many triangles can be approximate congruent to equilateral triangles? \nFor our proofs we use hypergraph Turán theory. This is joint work with Balogh and Dumitrescu.
URL:https://dimag.ibs.re.kr/event/2024-10-29/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20241022T163000
DTEND;TZID=Asia/Seoul:20241022T173000
DTSTAMP:20260416T073418
CREATED:20240905T081105Z
LAST-MODIFIED:20240913T030403Z
UID:9850-1729614600-1729618200@dimag.ibs.re.kr
SUMMARY:Colin Geniet\, Permutations\, patterns\, and twin-width
DESCRIPTION:This talk will first introduce combinatorics on permutations and patterns\, presenting the basic notions and some fundamental results: the Marcus-Tardos theorem which bounds the density of matrices avoiding a given pattern\, and the Guillemot-Marx algorithm for pattern detection using the notion now known as twin-width. \nI will then present a decomposition result: permutations avoiding a pattern factor into bounded products of separable permutations. This can be rephrased in terms of twin-width: permutation with bounded twin-width are build from a bounded product of permutations of twin-width 0. Comparable results on graph encodings follow from this factorisation. \nThis is joint work with Édouard Bonnet\, Romain Bourneuf\, and Stéphan Thomassé.
URL:https://dimag.ibs.re.kr/event/2024-10-22/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20241015T163000
DTEND;TZID=Asia/Seoul:20241015T173000
DTSTAMP:20260416T073418
CREATED:20240728T055631Z
LAST-MODIFIED:20240815T135958Z
UID:9631-1729009800-1729013400@dimag.ibs.re.kr
SUMMARY:Kyeongsik Nam (남경식)\, Random walks on percolation
DESCRIPTION:In general\, random walks on fractal graphs are expected to exhibit anomalous behaviors\, for example heat kernel is significantly different from that in the case of lattices. Alexander and Orbach in 1982 conjectured that random walks on critical percolation\, a prominent example of fractal graphs\, exhibit mean field behavior; for instance\, its spectral dimension is 4/3. In this talk\, I will talk about this conjecture for a canonical dependent percolation model.
URL:https://dimag.ibs.re.kr/event/2024-10-15/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20241008T163000
DTEND;TZID=Asia/Seoul:20241008T173000
DTSTAMP:20260416T073418
CREATED:20240815T140405Z
LAST-MODIFIED:20240815T140630Z
UID:9708-1728405000-1728408600@dimag.ibs.re.kr
SUMMARY:Mathias Schacht\, Canonical colourings in random graphs
DESCRIPTION:Rödl and Ruciński established Ramsey’s theorem for random graphs. In particular\, for fixed integers $r$\, $\ell\geq 2$ they showed that $n^{-\frac{2}{\ell+1}}$ is a threshold for the Ramsey property that every $r$-colouring of the edges of the binomial random graph $G(n\,p)$ yields a monochromatic copy of $K_\ell$. \nWe investigate how this result extends to arbitrary colourings of $G(n\,p)$ with an unbounded number of colours. In this situation Erdős and Rado showed that canonically coloured copies of $K_\ell$ can be ensured in the deterministic setting.\nWe transfer the Erdős-Rado theorem to the random environment and show that for $\ell\geq 4$ both thresholds coincide. As a consequence the proof yields $K_{\ell+1}$-free graphs $G$ for which every edge colouring yields a canonically coloured $K_\ell$. \nThis is joint work with Nina Kamčev.
URL:https://dimag.ibs.re.kr/event/2024-10-08/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20240924T163000
DTEND;TZID=Asia/Seoul:20240924T173000
DTSTAMP:20260416T073418
CREATED:20240721T112741Z
LAST-MODIFIED:20240913T040647Z
UID:9602-1727195400-1727199000@dimag.ibs.re.kr
SUMMARY:Gábor Tardos\, Extremal theory of 0-1 matrices
DESCRIPTION:We say that a 0-1 matrix A contains another such matrix (pattern) P if P can be obtained from a submatrix of A by possibly changing a few 1 entries to 0. The main question of this theory is to estimate the maximal number of 1 entries in an n by n 0-1 matrix NOT containing a given pattern P. This question has very close connections to Turan type extremal graph theory and also to the Devenport-Schinzel theory of sequences. Results in the extremal theory of 0-1 matrices proved useful in attacking problems in far away fields as combinatorial geometry and the analysis of algorithms. \nThis talk will concentrate on acyclic patterns and survey some old and recent results in the area and will also contain several open problems.
URL:https://dimag.ibs.re.kr/event/2024-09-24/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20240910T163000
DTEND;TZID=Asia/Seoul:20240910T173000
DTSTAMP:20260416T073418
CREATED:20240807T055137Z
LAST-MODIFIED:20240807T083739Z
UID:9690-1725985800-1725989400@dimag.ibs.re.kr
SUMMARY:Zhihan Jin (金之涵)\, The Helly number of Hamming balls and related problems
DESCRIPTION:We prove the following variant of Helly’s classical theorem for Hamming balls with a bounded radius. For $n > t$ and any (finite or infinite) set $X$\, if in a family of Hamming balls of radius $t$ in $X$\, every subfamily of at most $2^{t+1}$ balls have a common point\, so do all members of the family. This is tight for all $|X| > 1$ and all $n > t$. The proof of the main result is based on a novel variant of the so-called dimension argument\, which allows one to prove upper bounds that do not depend on the dimension of the ambient space. We also discuss several related questions and connections to problems and results in extremal finite set theory and graph theory. This is joint work with N. Alon and B. Sudakov.
URL:https://dimag.ibs.re.kr/event/2024-09-10/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20240906T163000
DTEND;TZID=Asia/Seoul:20240906T173000
DTSTAMP:20260416T073418
CREATED:20240619T001339Z
LAST-MODIFIED:20240707T023728Z
UID:8770-1725640200-1725643800@dimag.ibs.re.kr
SUMMARY:Neal Bushaw\, Edge-colored Extremal Problems
DESCRIPTION:An edge-colored graph $H$ is called rainbow if all of its edges are given distinct colors.  An edge-colored graph $G$ is then called rainbow $H$-free when no copy of $H$ in $G$ is rainbow.  With this\, we define a graph $G$ to be rainbow $H$-saturated when there is some proper edge-coloring of $G$ which is rainbow $H$-free\, but for every pair of non-adjacent vertices $x\,y\in V(G)$\, the graph $G+xy$ formed by adding the edge $xy$ to $G$ cannot be given a rainbow $H$-free coloring.  We think of these graphs as edge-maximal rainbow $H$-free graphs.  (We note that here we make no restrictions on the colorings of $G+xy$ whatsoever\, except that they are proper colorings.  They may use any number of colors\, and need not be extensions of the original rainbow $H$-free coloring of $G$.)\n\nWith this framework in place\, we define the rainbow saturation number and rainbow extremal number to be the largest and smallest number of edges\, respectively\, among all $n$ vertex rainbow $H$-saturated graphs.  The latter of these was defined by Keevash\, Mubayi\, Sudakov\, and Verstraëte in 2007; the former was introduced by B.\, Johnston\, and Rombach in 2019.\n\n In this talk\, we discuss recent progress on both the rainbow saturation numbers and rainbow extremal numbers.  We also give several broad generalizations of these concepts and discuss many open problems.  This talk contains joint work with Vic Bednar (Furman)\, Dan Johnston (Trinity College\, CT)\, and Puck Rombach (Vermont).
URL:https://dimag.ibs.re.kr/event/2024-09-06/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20240903T163000
DTEND;TZID=Asia/Seoul:20240903T173000
DTSTAMP:20260416T073418
CREATED:20240319T124710Z
LAST-MODIFIED:20240707T023848Z
UID:8360-1725381000-1725384600@dimag.ibs.re.kr
SUMMARY:Amadeus Reinald\, Oriented trees in $O(k \sqrt{k})$-chromatic digraphs\, a subquadratic bound for Burr's conjecture
DESCRIPTION:In 1980\, Burr conjectured that every directed graph with chromatic number $2k-2$ contains any oriented tree of order $k$ as a subdigraph. Burr showed that chromatic number $(k-1)^2$ suffices\, which was improved in 2013 to $\frac{k^2}{2} – \frac{k}{2} + 1$ by Addario-Berry et al. \nIn this talk\, we give the first subquadratic bound for Burr’s conjecture\, by showing that every directed graph with chromatic number $8\sqrt{\frac{2}{15}} k \sqrt{k} + O(k)$ contains any oriented tree of order $k$. Moreover\, we provide improved bounds of $\sqrt{\frac{4}{3}} k \sqrt{k}+O(k)$ for arborescences\, and $(b-1)(k-3)+3$ for paths on $b$ blocks\, with $b\ge 2$.
URL:https://dimag.ibs.re.kr/event/2024-09-03/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;VALUE=DATE:20240828
DTEND;VALUE=DATE:20240831
DTSTAMP:20260416T073418
CREATED:20240117T144439Z
LAST-MODIFIED:20240705T154134Z
UID:8135-1724803200-1725062399@dimag.ibs.re.kr
SUMMARY:2024 Combinatorics Workshop (2024 조합론 학술대회)
DESCRIPTION:Website: https://cw2024.combinatorics.kr/ \nLocation\nChungbuk National University\, Cheongju\, Korea. \nAdvisory Committee\n\nCommittee of Discrete Mathematics\, The Korean Mathematical Society (Chair: Sang-il Oum\, IBS Discrete Mathematics Group / KAIST)\n\nSponsors\n\nIBS Discrete Mathematics Group.\nKorean Mathematical Society
URL:https://dimag.ibs.re.kr/event/2024-08-28/
LOCATION:Chungbuk National University
CATEGORIES:Workshops and Conferences
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20240827T163000
DTEND;TZID=Asia/Seoul:20240827T173000
DTSTAMP:20260416T073418
CREATED:20240530T224746Z
LAST-MODIFIED:20240729T124158Z
UID:8730-1724776200-1724779800@dimag.ibs.re.kr
SUMMARY:Dillon Mayhew\, Monadic second-order definability for gain-graphic matroids
DESCRIPTION:Every (finite) matroid consists of a (finite) set called the ground set\, and a collection of distinguished subsets called the independent sets. A classic example arises when the ground set is a finite set of vectors from a vector space\, and the independent subsets are exactly the subsets that are linearly independent. Any such matroid is said to be representable. We can think of a representable matroid as being a geometrical configuration where the points have been given coordinates from a field. Another important class arises when the points are given coordinates from a group. Such a class is said to be gain-graphic.  \nMonadic second-order logic is a natural language for matroid applications. In this language we are able to quantify only over subsets of the ground set. The importance of monadic second-order logic comes from its connections to the theory of computation\, as exemplified by Courcelle’s Theorem. This theorem provides polynomial-time algorithms for recognising properties defined in monadic second-order logic (as long as we impose a bound on the structural complexity of the input objects). It is natural to ask which classes of matroids can be defined by sentences in monadic second-order logic. When the class consists of the matroids that are coordinatized by a field we have a complete answer to this question. When the class is coordinatized by a group the problem becomes much harder. \nThis talk will contain a brief introduction to matroids. Based on work with Sapir Ben-Shahar\, Matt Conder\, Daryl Funk\, Angus Matthews\, Mike Newman\, and Gabriel Verret.
URL:https://dimag.ibs.re.kr/event/2024-08-27/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;VALUE=DATE:20240819
DTEND;VALUE=DATE:20240824
DTSTAMP:20260416T073418
CREATED:20240214T010957Z
LAST-MODIFIED:20240705T154107Z
UID:8250-1724025600-1724457599@dimag.ibs.re.kr
SUMMARY:2024 Workshop on (Mostly) Matroids
DESCRIPTION:The 2024 Workshop on (Mostly) Matroids will be held in-person at the Institute for Basic Science (IBS)\, Daejeon\, South Korea\, from August 19\, 2024 to August 23\, 2024. We expect that most people would arrive on Sunday\, August 18 and leave on Saturday\, August 24. \nOur hope is that this workshop will continue the tradition of previous workshops held in Sittard (2008)\, Maastricht (2010\,2012)\, Princeton (2014)\, Eindhoven(2016)\, Waterloo (2017)\, and Baton Rouge (2019). The focus will be on all aspects of matroid theory\, including its connection to graph theory\, algebraic geometry\, and other areas of mathematics. \n 
URL:https://dimag.ibs.re.kr/event/wmm2024/
LOCATION:IBS Science Culture Center
CATEGORIES:Workshops and Conferences
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20240813T163000
DTEND;TZID=Asia/Seoul:20240813T173000
DTSTAMP:20260416T073418
CREATED:20240621T071458Z
LAST-MODIFIED:20240726T000121Z
UID:8784-1723566600-1723570200@dimag.ibs.re.kr
SUMMARY:Peter Nelson\, Formalizing matroid theory in a proof assistant
DESCRIPTION:For the past few years\, I’ve been working on formalizing proofs in matroid theory using the Lean proof assistant. This has led me to many interesting and unexpected places. I’ll talk about what formalization looks like in practice from the perspective of a combinatorialist.
URL:https://dimag.ibs.re.kr/event/2024-08-13/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20240806T163000
DTEND;TZID=Asia/Seoul:20240806T173000
DTSTAMP:20260416T073418
CREATED:20240530T224927Z
LAST-MODIFIED:20240710T060308Z
UID:8733-1722961800-1722965400@dimag.ibs.re.kr
SUMMARY:Daniel Král'\, Matroid depth and width parameters
DESCRIPTION:Depth and width parameters of graphs\, e.g.\, tree-width\, path-width and tree-depth\, play a crucial role in algorithmic and structural graph theory. These notions are of fundamental importance in the theory of graph minors\, fixed parameter complexity and the theory of sparsity. \nIn this talk\, we will survey structural and algorithmic results that concern width and depth parameters of matroids. We will particularly focus on matroid depth parameters and discuss the relation of the presented concepts to discrete optimization. As an application\, we will present matroid based algorithms that uncover a hidden Dantzig-Wolfe-like structure of an input instance (if such structure is present) and transform instances of integer programming to equivalent ones\, which are amenable to the existing tools in integer programming. \nThe most recent results presented in the talk are based on joint work with Marcin Briański\, Jacob Cooper\, Timothy F. N. Chan\, Martin Koutecký\, Ander Lamaison\, Kristýna Pekárková and Felix Schröder.
URL:https://dimag.ibs.re.kr/event/2024-08-06/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20240730T163000
DTEND;TZID=Asia/Seoul:20240730T173000
DTSTAMP:20260416T073418
CREATED:20240417T003214Z
LAST-MODIFIED:20240705T153017Z
UID:8532-1722357000-1722360600@dimag.ibs.re.kr
SUMMARY:Euiwoong Lee (이의웅)\, Parameterized Approximability of F-Deletion Problems
DESCRIPTION:For a family F of graphs\, the F-Deletion Problem asks to remove the minimum number of vertices from a given graph G to ensure that G belongs to F. One of the most common ways to obtain an interesting family F is to fix another family H of graphs and let F be the set of graphs that do not contain any graph H as some notion of a subgraph\, including (standard) subgraph\, induced subgraph\, and minor. This framework captures numerous basic graph problems\, including Vertex Cover\, Feedback Vertex Set\, and Treewidth Deletion\, and provides an interesting forum where ideas from approximation and parameterized algorithms influence each other. In this talk\, I will give a brief survey on the state of the art on the F-Deletion Problems for the above three notions of subgraphs\, and talk about a recent result on Weighted Bond Deletion.
URL:https://dimag.ibs.re.kr/event/2024-07-30/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;VALUE=DATE:20240729
DTEND;VALUE=DATE:20240803
DTSTAMP:20260416T073418
CREATED:20240126T071556Z
LAST-MODIFIED:20240705T154124Z
UID:8206-1722211200-1722643199@dimag.ibs.re.kr
SUMMARY:2024 Korean Student Combinatorics Workshop (KSCW2024\, 2024 조합론 학생 워크샵)
DESCRIPTION:Venue\nGongju Hanok Vilage (공주한옥마을) \nOrganizers\n\nDonggyu Kim (김동규)\, KAIST and IBS Discrete Mathematics Group\nSeokbeom Kim (김석범)\, KAIST and IBS Discrete Mathematics Group\nSeonghyuk Im (임성혁)\, KAIST and IBS Extremal Combinatorics and Probability Group\nHyunwoo Lee (이현우)\, KAIST and IBS Extremal Combinatorics and Probability Group\n\n 
URL:https://dimag.ibs.re.kr/event/kscw2024/
LOCATION:Gongju Hanok Village\, Gongju
CATEGORIES:Workshops and Conferences
END:VEVENT
BEGIN:VEVENT
DTSTART;VALUE=DATE:20240722
DTEND;VALUE=DATE:20240727
DTSTAMP:20260416T073418
CREATED:20240410T044447Z
LAST-MODIFIED:20240705T153024Z
UID:8506-1721606400-1722038399@dimag.ibs.re.kr
SUMMARY:2024 Summer School on Combinatorics and Algorithms (2024 조합론 및 알고리즘 여름학교)
DESCRIPTION:The 2024 Summer School on Combinatorics and Algorithms is a venue for students and early-career researchers to learn selected topics in theoretical computer science and discrete mathematics. It will be a great opportunity for young and aspiring researchers to study topics which are important but not covered during the lectures in the university classes. This summer\, two lecture series\, combinatorial optimization and grid minor theorem\, will be given by two leading experts on the subjects. There will be exercise sessions where you form a team and solve challenging questions related to the lecture subjects. \nWebsite: https://combialgo.dimag.kr/ \nLecturers and Topics\n\nChien-Chung Huang (ENS Paris\, France): Combinatorial Optimization\n\nThis lecture (12.5h) will cover essential topics in combinatorial optimization including: Berge’s theorem\, Konig’s theorem\, Egervary’s theorem\, Karger’s min-cut algorithm and Gomory-Hu trees\, Edmonds’ blossom algorithm for maximum matching\, matroid 101\, multi-commodity flow and k-coverage problems. \n\nSebastian Wiederrecht (DIMAG-IBS\, Korea): From treewidth to grid minor theorem\n\nThis lecture (6h) will present the notion of tree decomposition\, treewidth and graph minor\, and introduce the grid minor theorem by Robertson and Seymour. Grid minor theory is deemed as one of the most important theory in modern graph theory and has many applications in algorithms design\, data structure\, logic\, etc.
URL:https://dimag.ibs.re.kr/event/2024-07-22/
LOCATION:Bldg. N1\, KAIST
CATEGORIES:Workshops and Conferences
ORGANIZER;CN="Eunjung Kim (%EA%B9%80%EC%9D%80%EC%A0%95)":MAILTO:eunjungkim78@gmail.com
END:VEVENT
BEGIN:VEVENT
DTSTART;VALUE=DATE:20240715
DTEND;VALUE=DATE:20240720
DTSTAMP:20260416T073418
CREATED:20231122T060655Z
LAST-MODIFIED:20240705T155117Z
UID:7939-1721001600-1721433599@dimag.ibs.re.kr
SUMMARY:IBS-DIMAG workshop on combinatorics and geometric measure theory
DESCRIPTION:Website: https://cgmt.dimag.kr/ \nArrival Date: July 14\, 2024 Sunday. \nDeparture Date: July 20\, 2024 Saturday. \nOrganizers \n\nBen Lund (IBS Discrete Mathematics Group)\nDoowon Koh (Chungbuk National University)\nSang-il Oum (IBS Discrete Mathematics Group / KAIST)
URL:https://dimag.ibs.re.kr/event/2024-07-15/
LOCATION:Room B109\, IBS (기초과학연구원)
CATEGORIES:Workshops and Conferences
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20240705T163000
DTEND;TZID=Asia/Seoul:20240705T173000
DTSTAMP:20260416T073418
CREATED:20240613T134309Z
LAST-MODIFIED:20240705T152046Z
UID:8763-1720197000-1720200600@dimag.ibs.re.kr
SUMMARY:Hyunwoo Lee (이현우)\, Random matchings in linear hypergraphs
DESCRIPTION:For a given hypergraph $H$ and a vertex $v\in V(H)$\, consider a random matching $M$ chosen uniformly from the set of all matchings in $H.$ In $1995\,$ Kahn conjectured that if $H$ is a $d$-regular linear $k$-uniform hypergraph\, the probability that $M$ does not cover $v$ is $(1 + o_d(1))d^{-1/k}$ for all vertices $v\in V(H)$. This conjecture was proved for $k = 2$ by Kahn and Kim in 1998. In this paper\, we disprove this conjecture for all $k \geq 3.$ For infinitely many values of $d\,$ we construct $d$-regular linear $k$-uniform hypergraph $H$ containing two vertices $v_1$ and $v_2$ such that $\mathcal{P}(v_1 \notin M) = 1 – \frac{(1 + o_d(1))}{d^{k-2}}$ and $\mathcal{P}(v_2 \notin M) = \frac{(1 + o_d(1))}{d+1}.$ The gap between $\mathcal{P}(v_1 \notin M)$ and $\mathcal{P}(v_2 \notin M)$ in this $H$ is best possible. In the course of proving this\, we also prove a hypergraph analog of Godsil’s result on matching polynomials and paths in graphs\, which is of independent interest.
URL:https://dimag.ibs.re.kr/event/2024-07-05/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20240702T163000
DTEND;TZID=Asia/Seoul:20240702T173000
DTSTAMP:20260416T073418
CREATED:20240403T041848Z
LAST-MODIFIED:20240705T153033Z
UID:8483-1719937800-1719941400@dimag.ibs.re.kr
SUMMARY:Kisun Lee (이기선)\, Symmetric Tropical Rank 2 Matrices
DESCRIPTION:Tropical geometry replaces usual addition and multiplication with tropical addition (the min) and tropical multiplication (the sum)\, which offers a polyhedral interpretation of algebraic variety. This talk aims to pitch the usefulness of tropical geometry in understanding classical algebraic geometry. As an example\, we introduce the tropicalization of the variety of symmetric rank 2 matrices. We discuss that this tropicalization has a simplicial complex structure as the space of symmetric bicolored trees. As a result\, we show that this space is shellable and delve into its matroidal structure. It is based on the joint work with May Cai and Josephine Yu.
URL:https://dimag.ibs.re.kr/event/2024-07-02/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20240628T163000
DTEND;TZID=Asia/Seoul:20240628T173000
DTSTAMP:20260416T073418
CREATED:20240620T045259Z
LAST-MODIFIED:20240705T151013Z
UID:8775-1719592200-1719595800@dimag.ibs.re.kr
SUMMARY:Wonwoo Kang (강원우)\, Skein relations for punctured surfaces
DESCRIPTION:Since the introduction of cluster algebras by Fomin and Zelevinsky in 2002\, there has been significant interest in cluster algebras of surface type. These algebras are particularly noteworthy due to their ability to construct various combinatorial structures like snake graphs\, T-paths\, and posets\, which are useful for proving key structural properties such as positivity or the existence of bases. In this talk\, we will begin by presenting a cluster expansion formula that integrates the work of Musiker\, Schiffler\, and Williams with contributions from Wilson\, utilizing poset representatives for arcs on triangulated surfaces. Using these posets and the expansion formula as tools\, we will demonstrate skein relations\, which resolve intersections or incompatibilities between arcs. Topologically\, a skein relation replaces intersecting arcs or arcs with self-intersections with two sets of arcs that avoid the intersection differently. Additionally\, we will show that all skein relations on punctured surfaces include a term that is not divisible by any coefficient variable. Consequently\, we will see that the bangles and bracelets form spanning sets and exhibit linear independence. This work is done in collaboration with Esther Banaian and Elizabeth Kelley.
URL:https://dimag.ibs.re.kr/event/2024-06-28/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20240618T163000
DTEND;TZID=Asia/Seoul:20240618T173000
DTSTAMP:20260416T073418
CREATED:20240330T144427Z
LAST-MODIFIED:20240707T071910Z
UID:8450-1718728200-1718731800@dimag.ibs.re.kr
SUMMARY:Semin Yoo (유세민)\, Paley-like quasi-random graphs arising from polynomials
DESCRIPTION:We provide new constructions of families of quasi-random graphs that behave like Paley graphs but are neither Cayley graphs nor Cayley sum graphs. These graphs give a unified perspective of studying various graphs defined by polynomials over finite fields\, such as Paley graphs\, Paley sum graphs\, and graphs associated with Diophantine tuples and their generalizations from number theory. As an application\, we provide new lower bounds on the clique number and independence number of general quasi-random graphs. In particular\, we give a sufficient condition for the clique number of quasi-random graphs of order $n$ to be at least $(1-o(1))\log_{3.008}n$. Such a condition applies to many classical quasi-random graphs\, including Paley graphs and Paley sum graphs\, as well as some new Paley-like graphs we construct. If time permits\, we also discuss some problems of diophantine tuples arising from number theory\, which is our original motivation. \nThis is joint work with Seoyoung Kim and Chi Hoi Yip.
URL:https://dimag.ibs.re.kr/event/2024-06-18/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20240611T163000
DTEND;TZID=Asia/Seoul:20240611T173000
DTSTAMP:20260416T073418
CREATED:20240220T031718Z
LAST-MODIFIED:20240705T154023Z
UID:8279-1718123400-1718127000@dimag.ibs.re.kr
SUMMARY:Maria Chudnovsky\, Anticomplete subgraphs of large treewidth
DESCRIPTION:We will discuss recent progress on the topic of induced subgraphs and tree-decompositions. In particular this talk with focus on the proof of a conjecture of Hajebi that asserts that (if we exclude a few obvious counterexamples) for every integer t\, every graph with large enough treewidth contains two anticomplete induced subgraphs each of treewidth at least t. This is joint work with Sepher Hajebi and Sophie Spirkl.
URL:https://dimag.ibs.re.kr/event/2024-06-11/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20240604T163000
DTEND;TZID=Asia/Seoul:20240604T173000
DTSTAMP:20260416T073418
CREATED:20240327T044132Z
LAST-MODIFIED:20240707T071933Z
UID:8429-1717518600-1717522200@dimag.ibs.re.kr
SUMMARY:Jane Tan\, Semi-strong colourings of hypergraphs
DESCRIPTION:A vertex colouring of a hypergraph is $c$-strong if every edge $e$ sees at least $\min\{c\, |e|\}$ distinct colours. Let $\chi(t\,c)$ denote the least number of colours needed so that every $t$-intersecting hypergraph has a $c$-strong colouring. In 2012\, Blais\, Weinstein and Yoshida introduced this parameter and initiated study on when $\chi(t\,c)$ is finite: they showed that $\chi(t\,c)$ is finite whenever $t \geq c$ and unbounded when $t\leq c-2$. The boundary case $\chi(c-1\, c)$ has remained elusive for some time: $\chi(1\,2)$ is known to be finite by an easy classical result\, and $\chi(2\,3)$ was shown to be finite by Chung and independently by Colucci and Gyárfás in 2013. In this talk\, we present some recent work with Kevin Hendrey\, Freddie Illingworth and Nina Kamčev in which we fill in this gap by showing that $\chi(c-1\, c)$ is finite in general.
URL:https://dimag.ibs.re.kr/event/2024-06-04/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20240528T163000
DTEND;TZID=Asia/Seoul:20240528T173000
DTSTAMP:20260416T073418
CREATED:20240418T043152Z
LAST-MODIFIED:20240705T153011Z
UID:8542-1716913800-1716917400@dimag.ibs.re.kr
SUMMARY:Yongho Shin (신용호)\, Three-way online correlated selection
DESCRIPTION:Two-way online correlated selection (two-way OCS) is an online algorithm that\, at each timestep\, takes a pair of elements from the ground set and irrevocably chooses one of the two elements\, while ensuring negative correlation in the algorithm’s choices. OCS was initially invented by Fahrbach\, Huang\, Tao\, and Zadimoghaddam (FOCS 2020\, JACM 2022) to break a natural long-standing barrier in edge-weighted online bipartite matching. They posed two open questions\, one of which was the following: Can we obtain n-way OCS for $n >2$\, in which the algorithm can be given $n >2$ elements to choose from at each timestep? \nIn this talk\, we affirmatively answer this open question by presenting a three-way OCS which is simple to describe: it internally runs two instances of two-way OCS\, one of which is fed with the output of the other. Contrast to its simple construction\, we face a new challenge in analysis that the final output probability distribution of our three-way OCS is highly elusive since it requires the actual output distribution of two-way OCS. We show how we tackle this challenge by approximating the output distribution of two-way OCS by a flatter distribution serving as a safe surrogate. \nThis is joint work with Hyung-Chan An.
URL:https://dimag.ibs.re.kr/event/2024-05-28/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20240521T163000
DTEND;TZID=Asia/Seoul:20240521T173000
DTSTAMP:20260416T073418
CREATED:20231128T002423Z
LAST-MODIFIED:20240705T155114Z
UID:7965-1716309000-1716312600@dimag.ibs.re.kr
SUMMARY:Vadim Lozin\, Graph problems and monotone classes
DESCRIPTION:Very little is known about critical properties of graphs in the hierarchy of monotone classes\, i.e. classes closed under taking (not necessarily induced) subgraphs. We distinguish four important levels in this hierarchy and discuss possible new levels by focusing on the Hamiltonian cycle problem. In particular\, we obtain a number of results for this problem on monotone classes.
URL:https://dimag.ibs.re.kr/event/2024-05-21/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20240514T163000
DTEND;TZID=Asia/Seoul:20240514T173000
DTSTAMP:20260416T073418
CREATED:20240329T053414Z
LAST-MODIFIED:20240705T153041Z
UID:8445-1715704200-1715707800@dimag.ibs.re.kr
SUMMARY:Niloufar Fuladi\, Cross-cap drawings and signed reversal distance
DESCRIPTION:A cross-cap drawing of a graph G is a drawing on the sphere with g distinct points\, called cross-caps\, such that the drawing is an embedding except at the cross-caps\, where edges cross properly. A cross-cap drawing of a graph G with g cross-caps can be used to represent an embedding of G on a non-orientable surface of genus g. Mohar conjectured that any triangulation of a non-orientable surface of genus g admits a cross-cap drawing with g cross-caps in which each edge of the triangulation enters each cross-cap at most once. Motivated by Mohar’s conjecture\, Schaefer and Stefankovic provided an algorithm that computes a cross-cap drawing with a minimal number of cross-caps for a graph G such that each edge of the graph enters each cross-cap at most twice. In this talk\, I will first outline a connection between cross-cap drawings and an algorithm coming from computational biology to compute the signed reversal distance between two permutations. This connection will then be leveraged to answer two computational problems on graphs embedded on surfaces. \nFirst\, I show how to compute a “short” canonical decomposition for a non-orientable surface with a graph embedded on it. Such canonical decompositions were known for orientable surfaces\, but the techniques used to compute them do not generalize to non-orientable surfaces due to their more complex nature. Second\, I explain how to build a counter example to a stronger version of Mohar’s conjecture that is stated for pseudo-triangulations. \nThis is joint work with Alfredo Hubard and Arnaud de Mesmay.
URL:https://dimag.ibs.re.kr/event/2024-05-14/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20240507T163000
DTEND;TZID=Asia/Seoul:20240507T173000
DTSTAMP:20260416T073418
CREATED:20240327T080653Z
LAST-MODIFIED:20240705T153041Z
UID:8434-1715099400-1715103000@dimag.ibs.re.kr
SUMMARY:Tony Huynh\, Aharoni's rainbow cycle conjecture holds up to an additive constant
DESCRIPTION:In 2017\, Aharoni proposed the following generalization of the Caccetta-Häggkvist conjecture for digraphs. If G is a simple n-vertex edge-colored graph with n color classes of size at least r\, then G contains a rainbow cycle of length at most ⌈n/r⌉. \nIn this talk\, we prove that Aharoni’s conjecture holds up to an additive constant. Specifically\, we show that for each fixed r\, there exists a constant c such that if G is a simple n-vertex edge-colored graph with n color classes of size at least r\, then G contains a rainbow cycle of length at most n/r+c. \nThis is joint work with Patrick Hompe.
URL:https://dimag.ibs.re.kr/event/2024-05-07/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20240430T163000
DTEND;TZID=Asia/Seoul:20240430T173000
DTSTAMP:20260416T073418
CREATED:20240215T002334Z
LAST-MODIFIED:20240707T072159Z
UID:8252-1714494600-1714498200@dimag.ibs.re.kr
SUMMARY:Maximilian Gorsky\, Towards the half-integral Erdős-Pósa property for even dicycles
DESCRIPTION:A family $\mathcal F$ of (di)graphs is said to have the half- or quarter-integral Erdős-Pósa property if\, for any integer $k$ and any (di)graph $G$\, there either exist $k$ copies of graphs in $\mathcal F$ within $G$ such that any vertex of $G$ is contained in at most 2\, respectively at most 4\, of these copies\, or there exists a vertex set $A$ of size at most $f(k)$ such that $G – A$ contains no copies of graphs in $\mathcal F$. Very recently we showed that even dicycles have the quarter-integral Erdős-Pósa property [STOC’24] via the proof of a structure theorem for digraphs without large packings of even dicycles. \nIn this talk we discuss our current effort to improve this approach towards the half-integral Erdős-Pósa property\, which would be best possible\, as even dicycles do not have the integral Erdős-Pósa property. Complementing the talk given by Sebastian Wiederrecht in this seminar regarding our initial result\, we also shine a light on some of the particulars of the embedding we use in lieu of flatness and how this helps us to move even dicycles through the digraph. In the process of this\, we highlight the parts of the proof that initially caused the result to be quarter-integral. \n(This is joint work with Ken-ichi Kawarabayashi\, Stephan Kreutzer\, and Sebastian Wiederrecht.)
URL:https://dimag.ibs.re.kr/event/2024-04-30/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20240423T163000
DTEND;TZID=Asia/Seoul:20240423T173000
DTSTAMP:20260416T073418
CREATED:20240325T144336Z
LAST-MODIFIED:20240705T153042Z
UID:8410-1713889800-1713893400@dimag.ibs.re.kr
SUMMARY:Víctor Dalmau\, Right-adjoints of Datalog Programs
DESCRIPTION:We say that two functors Λ and Γ between thin categories of relational structures are adjoint if for all structures A and B\, we have that Λ(A) maps homomorphically to B if and only if A maps homomorphically to Γ(B). If this is the case Λ is called the left adjoint to Γ and Γ the right adjoint to Λ. In 2015\, Foniok and Tardif described some functors on the category of digraphs that allow both left and right adjoints. The main contribution of Foniok and Tardif is a construction of right adjoints to some of the functors identified as right adjoints by Pultr in 1970. We shall present several recent advances in this direction including a new approach based on the notion of Datalog Program borrowed from logic.
URL:https://dimag.ibs.re.kr/event/2024-04-23/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20240416T163000
DTEND;TZID=Asia/Seoul:20240416T173000
DTSTAMP:20260416T073418
CREATED:20240108T120038Z
LAST-MODIFIED:20240707T072207Z
UID:8112-1713285000-1713288600@dimag.ibs.re.kr
SUMMARY:Magnus Wahlström\, Algorithmic aspects of linear delta-matroids
DESCRIPTION:Delta-matroids are a generalization of matroids with connections to many parts of graph theory and combinatorics (such as matching theory and the structure of topological graph embeddings). Formally\, a delta-matroid is a pair $D=(V\,\mathcal F)$ where $\mathcal F$ is a collection of subsets of V known as “feasible sets.” (They can be thought of as generalizing the set of bases of a matroid\, while relaxing the condition that all bases must have the same cardinality.) \nLike with matroids\, an important class of delta-matroids are linear delta-matroids\, where the feasible sets are represented via a skew-symmetric matrix. Prominent examples of linear delta-matroids include linear matroids and matching delta-matroids (where the latter are represented via the famous Tutte matrix). \nHowever\, the study of algorithms over delta-matroids seems to have been much less developed than over matroids. \nIn this talk\, we review recent results on representations of and algorithms over linear delta-matroids. We first focus on classical polynomial-time aspects. We present a new (equivalent) representation of linear delta-matroids that is more suitable for algorithmic purposes\, and we show that so-called delta-sums and unions of linear delta-matroids are linear. As a result\, we get faster (randomized) algorithms for Linear Delta-matroid Parity and Linear Delta-matroid Intersection\, improving results from Geelen et al. (2004). \nWe then move on to parameterized complexity aspects of linear delta-matroids. We find that many results regarding linear matroids which have had applications in FPT algorithms and kernelization directly generalize to linear delta-matroids of bounded rank. On the other hand\, unlike with matroids\, there is a significant difference between the “rank” and “cardinality” parameters – the structure of bounded-cardinality feasible sets in a delta-matroid of unbounded rank is significantly harder to deal with than feasible sets in a bounded-rank delta-matroid.
URL:https://dimag.ibs.re.kr/event/2024-04-16/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
END:VCALENDAR