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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:20210101T000000
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END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220502T163000
DTEND;TZID=Asia/Seoul:20220502T173000
DTSTAMP:20260420T084722
CREATED:20220502T073000Z
LAST-MODIFIED:20240707T080029Z
UID:5511-1651509000-1651512600@dimag.ibs.re.kr
SUMMARY:Cheolwon Heo (허철원)\, The complexity of the matroid-homomorphism problems
DESCRIPTION:In this talk\, we introduce homomorphisms between binary matroids that generalize graph homomorphisms. For a binary matroid $N$\, we prove a complexity dichotomy for the problem $\rm{Hom}_\mathbb{M}(N)$ of deciding if a binary matroid $M$ admits a homomorphism to $N$. The problem is polynomial-time solvable if $N$ has a loop or has no circuits of odd length\, and is otherwise $\rm{NP}$-complete. We also get dichotomies for the list\, extension\, and retraction versions of the problem.\nThis is joint work with Hyobin Kim and Mark Siggers at Kyungpook National University.
URL:https://dimag.ibs.re.kr/event/2022-05-02/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220509T163000
DTEND;TZID=Asia/Seoul:20220509T173000
DTSTAMP:20260420T084722
CREATED:20220509T073000Z
LAST-MODIFIED:20240705T173026Z
UID:5524-1652113800-1652117400@dimag.ibs.re.kr
SUMMARY:Kyeongsik Nam (남경식)\, Large deviations for subgraph counts in random graphs
DESCRIPTION:The upper tail problem for subgraph counts in the Erdos-Renyi graph\, introduced by Janson-Ruciński\, has attracted a lot of attention. There is a class of Gibbs measures associated with subgraph counts\, called exponential random graph model (ERGM). Despite its importance\, lots of fundamental questions have remained unanswered owing to the lack of exact solvability. In this talk\, I will talk about a brief overview on the upper tail problem and the concentration of measure results for the ERGM. Joint work with Shirshendu Ganguly and Ella Hiesmayr.
URL:https://dimag.ibs.re.kr/event/2022-05-09/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220516T163000
DTEND;TZID=Asia/Seoul:20220516T173000
DTSTAMP:20260420T084722
CREATED:20220516T073000Z
LAST-MODIFIED:20240707T080014Z
UID:5553-1652718600-1652722200@dimag.ibs.re.kr
SUMMARY:Andreas Holmsen\, A colorful version of the Goodman-Pollack-Wenger transversal theorem
DESCRIPTION:Hadwiger’s transversal theorem gives necessary and sufficient conditions for the existence of a line transversal to a family of pairwise disjoint convex sets in the plane. These conditions were subsequently generalized to hyperplane transversals in $\mathbb{R}^d$ by Goodman\, Pollack\, and Wenger. Here we establish a colorful extension of their theorem\, which proves a conjecture of Arocha\, Bracho\, and Montejano. The proof uses topological methods\, in particular the Borsuk-Ulam theorem. The same methods also allow us to generalize some colorful transversal theorems of Montejano and Karasev.
URL:https://dimag.ibs.re.kr/event/2022-05-16/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220518T163000
DTEND;TZID=Asia/Seoul:20220518T173000
DTSTAMP:20260420T084722
CREATED:20220518T073000Z
LAST-MODIFIED:20240705T173008Z
UID:5506-1652891400-1652895000@dimag.ibs.re.kr
SUMMARY:Jan Kurkofka\, Canonical Graph Decompositions via Coverings
DESCRIPTION:We present a canonical way to decompose finite graphs into highly connected local parts. The decomposition depends only on an integer parameter whose choice sets the intended degree of locality. The global structure of the graph\, as determined by the relative position of these parts\, is described by a coarser model. This is a simpler graph determined entirely by the decomposition\, not imposed. \nThe model and decomposition are obtained as projections of the tangle-tree structure of a covering of the given graph that reflects its local structure at the intended level of locality while unfolding its global structure. \nOur theorem extends to locally finite quasi-transitive graphs and in particular to locally finite Cayley graphs. It thereby offers a canonical decomposition theorem for finitely generated groups into local parts\, whose relative structure is displayed by a graph. \nJoint work with Reinhard Diestel\, Raphael W. Jacobs and Paul Knappe.
URL:https://dimag.ibs.re.kr/event/2022-05-18/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220519T161500
DTEND;TZID=Asia/Seoul:20220519T171500
DTSTAMP:20260420T084722
CREATED:20220519T071500Z
LAST-MODIFIED:20240707T080000Z
UID:5661-1652976900-1652980500@dimag.ibs.re.kr
SUMMARY:Gil Kalai\, The Cascade Conjecture and other Helly-type Problems
DESCRIPTION:[Colloquium\, Department of Mathematical Sciences\, KAIST] \nFor a set $X$ of points $x(1)$\, $x(2)$\, $\ldots$\, $x(n)$ in some real vector space $V$ we denote by $T(X\,r)$ the set of points in $X$ that belong to the convex hulls of r pairwise disjoint subsets of $X$.\nWe let $t(X\,r)=1+\dim(T(X\,r))$. \nRadon’s theorem asserts that\nIf $t(X\,1)< |X|$\, then $t(X\, 2) >0$. \nThe first open case of the cascade conjecture asserts that\nIf $t(X\,1)+t(X\,2) < |X|$\, then $t(X\,3) >0$. \nIn the lecture\, I will discuss connections with topology and with various problems in graph theory. I will also mention questions regarding dimensions of intersection of convex sets. \nSome related material:\n1) A lecture (from 1999): An invitation to Tverberg Theorem: https://youtu.be/Wjg1_QwjUos\n2) A paper on Helly type problems by Barany and me https://arxiv.org/abs/2108.08804\n3) A link to Barany’s book: Combinatorial convexity https://www.amazon.com/Combinatorial-Convexity-University-Lecture-77/dp/1470467097
URL:https://dimag.ibs.re.kr/event/2022-05-19/
LOCATION:Zoom ID: 868 7549 9085
CATEGORIES:Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220523T163000
DTEND;TZID=Asia/Seoul:20220523T173000
DTSTAMP:20260420T084722
CREATED:20220523T073000Z
LAST-MODIFIED:20240705T172235Z
UID:5451-1653323400-1653327000@dimag.ibs.re.kr
SUMMARY:Stijn Cambie\, The precise diameter of reconfiguration graphs
DESCRIPTION:Reconfiguration is about changing instances in small steps. For example\, one can perform certain moves on a Rubik’s cube\, each of them changing its configuration a bit. In this case\, in at most 20 steps\, one can end up with the preferred result. One could construct a graph with as nodes the possible configurations of the Rubik’s cube (up to some isomorphism) and connect two nodes if one can be obtained by applying only one move to the other. Finding an optimal solution\, i.e. a minimum number of moves to solve a Rubik’s cube is now equivalent to finding the distance in the graph. \nWe will wonder about similar problems in reconfiguration\, but applied to list- and DP-colouring. In this case\, the small step consists of recolouring precisely one vertex. Now we will be interested in the diameter of the reconfiguration graph and show that sometimes we can determine the precise diameters of these. \nAs such\, during this talk\, we present some main ideas of [arXiv:2204.07928].
URL:https://dimag.ibs.re.kr/event/2022-05-23/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220525T163000
DTEND;TZID=Asia/Seoul:20220525T173000
DTSTAMP:20260420T084722
CREATED:20220525T073000Z
LAST-MODIFIED:20240705T172235Z
UID:5509-1653496200-1653499800@dimag.ibs.re.kr
SUMMARY:Sebastian Siebertz\, Transducing paths in graph classes with unbounded shrubdepth
DESCRIPTION:Transductions are a general formalism for expressing transformations of graphs (and more generally\, of relational structures) in logic. We prove that a graph class C can be FO-transduced from a class of bounded-height trees (that is\, has bounded shrubdepth) if\, and only if\, from C one cannot FO-transduce the class of all paths. This establishes one of the three remaining open questions posed by Blumensath and Courcelle about the MSO-transduction quasi-order\, even in the stronger form that concerns FO-transductions instead of MSO-transductions. \nThe backbone of our proof is a graph-theoretic statement that says the following: If a graph G excludes a path\, the bipartite complement of a path\, and a half-graph as semi-induced subgraphs\, then the vertex set of G can be partitioned into a bounded number of parts so that every part induces a cograph of bounded height\, and every pair of parts semi-induce a bi-cograph of bounded height. This statement may be of independent interest; for instance\, it implies that the graphs in question form a class that is linearly chi-bounded. \nThis is joint work with Patrice Ossona de Mendez and Michał Pilipczuk.
URL:https://dimag.ibs.re.kr/event/2022-05-25/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220527T132000
DTEND;TZID=Asia/Seoul:20220527T174000
DTSTAMP:20260420T084722
CREATED:20220527T042000Z
LAST-MODIFIED:20240707T075940Z
UID:5555-1653657600-1653673200@dimag.ibs.re.kr
SUMMARY:KSIAM 2022 Spring Meeting
DESCRIPTION:KSIAM (Korean Society for Industrial and Applied Mathematics) will have the KSIAM 2022 Spring Conference at the Institute for Basic Science (IBS). Its academic session for Combinatorics decided to have an invited talk by Joonkyung Lee at the Hanyang University\, a special session “Graph Theory” organized by Sang-il Oum and the IBS DIMAG\, a special session “Enumerative Combinatorics” organized by Dongsu Kim at KAIST\, and a poster session\, all on May 27 afternoon. The deadline for the abstract submission is May 2 and the deadline for the early registration is May 9. \nInvited talk (May 27 Friday\, 16:40-17:40)\n\nJoonkyung Lee이준경 (Hanyang University)\, Graph homomorphism inequalities and their applications\nCounting (weighted) homomorphisms between graphs relates to a wide variety of areas\, in- cluding graph theory\, probability\, statistical physics and theoretical computer science. In recent years\, various new applications of inequalities between graph homomorphism counts have been found.\nWe will discuss some of the examples\, including a simple proof of the Bondy–Simonovits theorem and a new estimate for the rainbow Turán numbers of even cycles. If time permits\, we will also touch upon some recent progress on Sidorenko’s conjecture and related questions\, in particular their applications on the bipartite Turán problems.\nBased on joint work with David Conlon\, Jaehoon Kim\, Hong Liu\, and Tuan Tran. \n\nSpecial session “Graph Theory” (May 27\, 13:20-14:40)\nOrganized by Sang-il Oum엄상일 (IBS Discrete Mathematics Group & KAIST). \nSpeakers\n\nBoram Park박보람 (Ajou University)\, Odd Coloring of Graphs\nAn odd $c$-coloring of a graph is a proper $c$-coloring such that each non-isolated vertex has a color appearing an odd number of times on its neighborhood. Recently\, Cranston investigated odd colorings of graphs with bounded maximum average degree\, and conjectured that every graph $G$ with $\operatorname{mad}(G)\leq \frac{4c-4}{c+1}$ has an odd $c$-coloring for $c\geq 4$\, and proved the conjecture for $c\in\{5\, 6\}$. In particular\, planar graphs with girth at least $7$ and $6$ have an odd $5$-coloring and an odd $6$-coloring\, respectively.\nWe completely resolve Cranston’s conjecture. For $c\geq 7$\, we show that the conjecture is true\, in a stronger form that was implicitly suggested by Cranston\, but for $c=4$\, we construct counterexamples\, which all contain $5$-cycles. On the other hand\, we show that a graph $G$ with $\operatorname{mad}(G)<\frac{22}{9}$ and no induced $5$-cycles has an odd $4$-coloring. This implies that a planar graph with girth at least 11 has an odd $4$-coloring. We also prove that a planar graph with girth at least 5 has an odd $6$-coloring.\nJoint work with Eun-Kyung Cho\, Ilkyoo Choi\, and Hyemin Kown. \n\n\nJongyook Park박종육 (Kyungpook National University)\, On the Delsarte bound\nWe study the order of a maximal clique in an amply regular graph with a fixed smallest eigenvalue by considering a vertex that is adjacent to some (but not all) vertices of the maximal clique. As a consequence\, we show that if a strongly regular graph contains a Delsarte clique\, then the parameter μ is either small or large. Furthermore\, we obtain a cubic polynomial that assures that a maximal clique in an amply regular graph is either small or large (under certain assumptions). Combining this cubic polynomial with the claw-bound\, we rule out an infinite family of feasible parameters (v\, k\, λ\, μ) for strongly regular graphs. Lastly\, we provide tables of parameters (v\, k\, λ\, μ) for nonexistent strongly regular graphs with smallest eigenvalue −4\,−5\,−6 or −7. This is joint work with Gary Greaves and Jack Koolen. \n\n\nO-joung Kwon권오정 (Hanyang University and IBS Discrete Mathematics Group)\, Well-partitioned chordal graphs\nWe introduce a new subclass of chordal graphs that generalizes the class of split graphs\, which we call well-partitioned chordal graphs. A connected graph $G$ is a well-partitioned chordal graph if there exist a partition $\mathcal{P}$ of the vertex set of $G$ into cliques and a tree $\mathcal{T}$ having $\mathcal{P}$ as a vertex set such that for distinct $X\,Y\in \mathcal{P}$\, (1) the edges between $X$ and $Y$ in $G$ form a complete bipartite subgraph whose parts are some subsets of $X$ and $Y$\, if $X$ and $Y$ are adjacent in $\mathcal{T}$\, and (2) there are no edges between $X$ and $Y$ in $G$ otherwise. A split graph with vertex partition $(C\, I)$ where $C$ is a clique and $I$ is an independent set is a well-partitioned chordal graph as witnessed by a star $\mathcal{T}$ having $C$ as the center and each vertex in $I$ as a leaf\, viewed as a clique of size $1$. We characterize well-partitioned chordal graphs by forbidden induced subgraphs\, and give a polynomial-time algorithm that given a graph\, either finds an obstruction\, or outputs a partition of its vertex set that asserts that the graph is well-partitioned chordal.\nWe observe that there are problems\, for instance Densest $k$-Subgraph and $b$-Coloring\, that are polynomial-time solvable on split graphs but become NP-hard on well-partitioned chordal graphs. On the other hand\, we show that the Geodetic Set problem\, known to be NP-hard on chordal graphs\, can be solved in polynomial time on well-partitioned chordal graphs. We also answer two combinatorial questions on well-partitioned chordal graphs that are open on chordal graphs\, namely that each well-partitioned chordal graph admits a polynomial-time constructible tree $3$-spanner\, and that each ($2$-connected) well-partitioned chordal graph has a vertex that intersects all its longest paths (cycles). Joint work with Jungho Ahn\, Lars Jaffke\, and Paloma T. Lima. \n\n\nStijn Cambie (IBS Extremal Combinatorics and Probability Group)\, Regular Cereceda’s Conjecture\nThe reconfiguration graph $\mathcal C_k(G)$ for the $k$-colourings of a graph $G$ has a vertex for each proper $k$-colouring of $G$\, and two vertices of $\mathcal C_k(G)$ are adjacent precisely when those $k$-colourings differ on a single vertex of $G$. Much work has focused on bounding the maximum value of $\operatorname{diam} \mathcal C_k(G)$ over all $n$-vertex graphs $G$. One of the most famous conjectures related related to $\mathcal C_k(G)$ is Cereceda’s conjecture\, which says that if $k \ge \operatorname{degen}(G) + 2$\, the diameter of $\mathcal C_k(G)$ is $O(n^2)$. In this talk\, we give some ideas towards a precise form for Cereceda’s conjecture\, when restricting to regular graphs. \nThis is based on joint work with Wouter Cames van Batenburg (TU Delft\, the Netherlands) and Daniel Cranston (Virginia Commonwealth University\, USA)\, which originates from the online workshop Graph Reconfiguration of the Sparse Graphs Coalition. \n\nSpecial session “Enumerative Combinatorics” (May 27\, 15:00-16:20)\nOrganized by Dongsu Kim김동수 (KAIST). \nSpeakers\n\nMeesue Yoo류미수 (Chungbuk National University)\, Combinatorial description for the Hall-Littlewood expansion of unicellular LLT and chromatic quasisymmetric polynomials\nIn this work\, we obtain a Hall–Littlewood expansion of the chromatic quasisymmetric functions by using a Dyck path model and linked rook placements. By using the Carlsson–Mellit relation between the chromatic quasisymmetric functions and the unicellular LLT polynomials\, this combinatorial description for the Hall–Littlewood coefficients of the chromatic quasisymmetric functions also gives the coefficients of the unicellular LLT polynomials expanded in terms of the modified transformed Hall–Littlewood polynomials. Joint work with Seung Jin Lee. \n\n\nDonghyun Kim김동현 (Sungkyunkwan University)\, Combinatorial formulas for the coefficients of the Al-Salam-Chihara polynomials\nThe Al-Salam-Chihara polynomials are an important family of orthogonal polynomials in one variable $x$ depending on 3 parameters $\alpha$\, $\beta$ and $q$. They are closely connected to a model from statistical mechanics called the partially asymmetric simple exclusion process (PASEP) and they can be obtained as a specialization of the Askey-Wilson polynomials. We give two different combinatorial formulas for the coefficients of the (transformed) Al-Salam-Chihara polynomials. Our formulas make manifest the fact that the coefficients are polynomials in $\alpha$\, $\beta$ and $q$ with positive coefficients. \n\n\nJisun Huh허지선 (Ajou University)\, Combinatorics on bounded Motzkin paths and its applications\nA free Motzkin path of length \(n\) is a lattice path which starts at \((0\,0)\) or \((0\,1)\)\, ends at \((n\,0)\)\, and has only up steps \(u=(1\,1)\)\, down steps \(d=(1\,-1)\)\, and flat steps \(f=(1\,0)\). In addition\, if a free Motzkin path starts at \((0\,0)\) and stays weakly above the \(x\)-axis\, then it is called a Motzkin path. In this talk\, we construct a bijection between \(F(m\,r\,k)\) and \(M(m\,r\,k)\)\, where \(F(m\,r\,k)\) is the set of free Motzkin paths of length \(m+r\) with \(r\) flat steps that are contained in the strip \(-\lfloor k/2 \rfloor \leq y \leq \lfloor (k+1)/2 \rfloor\) and \(M(m\,r\,k)\) is the set of Motzkin prefixed of length \(m+r\) with \(r\) flat steps that are contained in the strip \(0 \leq y \leq k\). Furthermore\, we provide path interpretations of ordinary/self-conjugate \(t\)-core partitions with \(m\)-corners as an application.\nThis is joint work with Hyunsoo Cho\, Hayan Nam\, and Jaebum Sohn. \n\n\nJihyeug Jang장지혁 (Sungkyunkwan University)\, A combinatorial model for the transition matrix between the Specht and web bases\nWe introduce a new class of permutations\, called web permutations. Using these permutations\, we provide a combinatorial interpretation for entries of the transition between the Specht and web bases\, which answers Rhoades’s question. Furthermore\, we study enumerative properties of these permutations. Joint work with Byung-Hak Hwang and Jaeseong Oh.
URL:https://dimag.ibs.re.kr/event/ksiam-2022-spring-meeting/
LOCATION:IBS Science Culture Center
CATEGORIES:Workshops and Conferences
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220530T163000
DTEND;TZID=Asia/Seoul:20220530T173000
DTSTAMP:20260420T084722
CREATED:20220530T073000Z
LAST-MODIFIED:20240705T172232Z
UID:5495-1653928200-1653931800@dimag.ibs.re.kr
SUMMARY:Hongseok Yang (양홍석)\, Learning Symmetric Rules with SATNet
DESCRIPTION:SATNet is a differentiable constraint solver with a custom backpropagation algorithm\, which can be used as a layer in a deep-learning system. It is a promising proposal for bridging deep learning and logical reasoning. In fact\, SATNet has been successfully applied to learn\, among others\, the rules of a complex logical puzzle\, such as Sudoku\, just from input and output pairs where inputs are given as images. In this paper\, we show how to improve the learning of SATNet by exploiting symmetries in the target rules of a given but unknown logical puzzle or more generally a logical formula. We present SymSATNet\, a variant of SATNet that translates the given symmetries of the target rules to a condition on the parameters of SATNet and requires that the parameters should have a particular parametric form that guarantees the condition. The requirement dramatically reduces the number of parameters to learn for the rules with enough symmetries\, and makes the parameter learning of SymSATNet much easier than that of SATNet. We also describe a technique for automatically discovering symmetries of the target rules from examples. Our experiments with Sudoku and Rubik’s cube show the substantial improvement of SymSATNet over the baseline SATNet. \nThis is joint work with Sangho Lim and Eungyeol Oh.
URL:https://dimag.ibs.re.kr/event/2022-05-30/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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