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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:20230101T000000
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END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20241008T163000
DTEND;TZID=Asia/Seoul:20241008T173000
DTSTAMP:20260416T073211
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:20241015T163000
DTEND;TZID=Asia/Seoul:20241015T173000
DTSTAMP:20260416T073211
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:20241022T163000
DTEND;TZID=Asia/Seoul:20241022T173000
DTSTAMP:20260416T073211
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:20241029T163000
DTEND;TZID=Asia/Seoul:20241029T173000
DTSTAMP:20260416T073211
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:20241105T163000
DTEND;TZID=Asia/Seoul:20241105T173000
DTSTAMP:20260416T073211
CREATED:20240718T042813Z
LAST-MODIFIED:20241022T011746Z
UID:9550-1730824200-1730827800@dimag.ibs.re.kr
SUMMARY:Michał Pilipczuk\, Monadic stability and monadic dependence
DESCRIPTION:We will give an overview of the recent attempts of building a structure theory for graphs centered around First-Order transductions: a notion of containment inspired by finite model theory. Particularly\, we will speak about the notions of monadic dependence and monadic stability\, their combinatorial characterizations\, and the developments on the algorithmic front.
URL:https://dimag.ibs.re.kr/event/2024-11-05/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20241111T110000
DTEND;TZID=Asia/Seoul:20241111T173000
DTSTAMP:20260416T073211
CREATED:20241101T055140Z
LAST-MODIFIED:20241111T080120Z
UID:10031-1731322800-1731346200@dimag.ibs.re.kr
SUMMARY:IBS-DIMAG Workshop on Topology and Combinatorics
DESCRIPTION:The IBS-DIMAG Workshop on Topology and Combinatorics will be held on November 11\, 2024 at Room B332\, Institute for Basic Science (IBS)\, Daejeon\, South Korea. \nInvited Speakers (tentative)\n\nKarim Adiprasito (Jussieu Institute of Mathematics)\nMinho Cho조민호 (IBS Extremal Combinatorics and Probability Group)\nNiloufar Fuladi (INRIA Center of Université de Lorraine)\nMinki Kim김민기 (GIST)\nDohyeon Lee이도현 (KAIST & IBS Discrete Mathematics Group)\nGeunho Lim임근호 (Jussieu Institute of Mathematics)\nSemin Yoo유세민 (IBS Discrete Mathematics Group)\n\nTentative Schedule\n\n11:00-11:30 Karim Adiprasito\, The Charney Davis conjecture and Boolean decompositions\n12:00-14:00 Lunch Break\n14:00-14:30 Niloufar Fuladi\, Universal families of arcs and curves on surfaces\n14:30-15:00 Semin Yoo유세민\, The Charney-Davis conjecture and its related complexes (survey)\n15:00-15:30 Geunho Lim임근호\, Bounds on Cheeger-Gromov invariants and simplicial complexity of triangulated manifolds\n15:30-16:00 Break\n16:00-16:30 Minki Kim김민기\, Some extensions of the colorful Helly theorem\n16:30-17:00 Minho Cho조민호\, Fractional Helly theorems via weak saturation\n17:00-17:30 Dohyeon Lee이도현\, Betti number of clique complex of H-free graphs (survey)\n18:00-20:00 Banquet\n\nOrganizer\n\nSemin Yoo유세민\, IBS Discrete Mathematics Group\n\nAbstracts\nKarim Adiprasito\, The Charney Davis conjecture and Boolean decompositions\nI will present a novel approach to the Charney Davis conjecture by introducing anticommutative Lefschetz properties\, and studying them on the Danzer complex of flag spheres. \nSemin Yoo\, The Charney-Davis conjecture and its related complexes (survey)\nThe Charney-Davis conjecture lies in the intersection between topology and combinatorics. The conjecture is a special case of the Hopf-Chern-Thurston conjecture for all nonpositively curved\, piecewise Euclidean manifolds which are cellulated by regular Euclidean cubes. In 2001\, Davis and Okun solved the conjecture for a 4-dimensional case\, and some other partial results are also known. However\, the conjecture is still open so far. \nIn this talk\, I will describe five statements that solve the Charney-Davis conjecture and explain some complexes to achieve this goal. \nNiloufar Fuladi\, Universal families of arcs and curves on surfaces\nIn this talk I introduce a family of curves that realize all pants decomposition of a surface: a family of simple closed curves Γ on a surface realizes all types of pants decompositions if for any pants decomposition of the surface\, there exists a homeomorphism sending it to a subset of the curves in Γ. The study of such universal families of curves is motivated by questions on graph embeddings\, joint crossing numbers and finding an elusive center of moduli space. I will discuss the case of surfaces without punctures\, where we establish an exponential upper bound and a superlinear lower bound on the minimum size of the family of curves with this universal property. I also talk about a similar concept of universality for triangulations of polygons\, where we provide bounds which are tight up to logarithmic factors. In this talk\, I will explain the background and context and no prior knowledge in topology or surfaces is needed. \nThis is joint work with Arnaud de Mesmay and Hugo Parlier. \nGeunho Lim\, Bounds on Cheeger-Gromov invariants and simplicial complexity of triangulated manifolds\nUsing L^2 cohomology\, Cheeger and Gromov define the L^2 rho-invariant on manifolds with arbitrary fundamental groups\, as a generalization of the Atiyah-Singer rho-invariant. There are many interesting applications in geometry\, topology\, and combinatorics. In this talk\, we show linear bounds on the rho-invariants in terms of simplicial complexity of manifolds by using hyperbolization methods. As applications\, we give new concrete examples in the complexity theory of high-dimensional (homotopy) lens spaces. This is a joint work with Shmuel Weinberger. \nMinki Kim\, Some extensions of the colorful Helly theorem\nGiven $k > d$ finite families of convex sets in $\mathbb{R}^d$\, if every colorful $(d+1)$-tuple is intersecting\, then the union of $k-d$ color classes is intersecting. This is known as the colorful Helly theorem. Based on recent joint work with Alan Lew\, I will present some extensions of the colorful Helly theorem and their applications. \nMinho Cho\, Fractional Helly theorems via weak saturation\nTwo celebrated extensions of the classical Helly’s theorem are the fractional Helly theorem and the colorful Helly theorem. Bulavka\, Goodarzi\, and Tancer recently established the optimal bound for the unified generalization of the fractional and the colorful Helly theorems using a colored extension of the exterior algebra. In this talk\, we introduce a combinatorial reduction of both the fractional Helly theorem and its colorful version to a classical problem in extremal combinatorics known as weak saturation. No such results connecting the fractional Helly theorem and weak saturation are known in the long history of literature. These reductions\, along with basic linear algebraic arguments for the reduced weak saturation problems\, let us give new short proofs of the optimal bounds for both the fractional Helly theorem and its colorful version without using exterior algebra. \nThis is joint work with Debsoumya Chakraborti\, Jinha Kim\, and Minki Kim. \nDohyeon Lee\, Betti number of clique complex of H-free graphs (survey)\nThe clique complex of a graph is a simplicial complex whose faces correspond to cliques of the given graph. In this talk\, we investigate extremal properties of the Betti numbers of clique complexes. While general simplicial complexes with n vertices can have a total Betti number approximately $2^n$\, Adamaszek showed that Betti number of clique complex is bounded by around $1.32^n$. Furthermore\, if the underlying graph has an independence number at most two\, the bound tightens to $1.25^n$. Adiprasito\, Nevo\, and Tancer established additional bounds on the total Betti number for clique complexes of (induced) H-free graphs for various graph H\, along with constructions of graphs with large total Betti number. In another direction\, Zhang and Wu demonstrated that for ternary graphs (whose with no induced cycles of length 3n)\, the Betti number of the independence complex (the clique complex of the complement of a graph) is at most one. Indeed\, Jinha Kim showed that these independence complexes are either contractible or homotopy spheres.
URL:https://dimag.ibs.re.kr/event/2024-11-11/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Workshops and Conferences
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20241112T163000
DTEND;TZID=Asia/Seoul:20241112T173000
DTSTAMP:20260416T073211
CREATED:20240831T051640Z
LAST-MODIFIED:20240917T095446Z
UID:9815-1731429000-1731432600@dimag.ibs.re.kr
SUMMARY:Karim Adiprasito\, Ehrhart theory revisited: Algebraic aspects\, unimodality and more
DESCRIPTION:Ehrhart theory is the study of lattice polytopes\, specifically aimed at understanding how many lattice points are inside dilates of a given lattice polytope\, and the study has a wide range of connections ranging from coloring graphs to mirror symmetry and representation theory. Recently\, we introduced new algebraic tools to understand this theory\, and resolve some classical conjectures. I will explain the combinatorial underpinnings behind two of the key techniques: Parseval identities for semigroup algebras\, and the character algebra of a semigroup.
URL:https://dimag.ibs.re.kr/event/2024-11-12/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20241126T163000
DTEND;TZID=Asia/Seoul:20241126T173000
DTSTAMP:20260416T073211
CREATED:20241018T131301Z
LAST-MODIFIED:20241018T132054Z
UID:9992-1732638600-1732642200@dimag.ibs.re.kr
SUMMARY:Eng Keat Hng\, Graphon branching processes and fractional isomorphism
DESCRIPTION:In 2005\, Bollobás\, Janson and Riordan introduced and extensively studied a general model of inhomogeneous random graphs parametrised by graphons. In particular\, they studied the emergence of a giant component in these inhomogeneous random graphs by relating them to a broad collection of inhomogeneous Galton-Watson branching processes. \nFractional isomorphism of finite graphs is an important and well-studied concept at the intersection of graph theory and combinatorial optimisation. It has many different characterizations that involve a range of very different and seemingly unrelated properties of graphs. Recently\, Grebík and Rocha developed a theory of fractional isomorphism for graphons. \nIn our work\, we characterise inhomogeneous random graphs that yield the same inhomogeneous Galton-Watson branching process (and hence have a similar component structure). \nThis is joint work with Jan Hladký and Anna Margarethe Limbach.
URL:https://dimag.ibs.re.kr/event/2024-11-26/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20241203T163000
DTEND;TZID=Asia/Seoul:20241203T173000
DTSTAMP:20260416T073211
CREATED:20241031T064935Z
LAST-MODIFIED:20241031T065407Z
UID:10022-1733243400-1733247000@dimag.ibs.re.kr
SUMMARY:Yulai Ma\, Pairwise disjoint perfect matchings in regular graphs
DESCRIPTION:An $r$-graph is an $r$-regular graph in which every odd set of vertices is connected to its complement by at least $r$ edges. A central question regarding $r$-graphs is determining the maximum number of pairwise disjoint perfect matchings they can contain. This talk explores how edge connectivity influences this parameter. \nFor ${0 \leq \lambda \leq r}$\, let $m(\lambda\,r)$ denote the maximum number $s$ such that every $\lambda$-edge-connected $r$-graph contains $s$ pairwise disjoint perfect matchings. The values of $m(\lambda\,r)$ are known only in limited cases; for example\, $m(3\,3)=m(4\,r)=1$\, and $m(r\,r) \leq r-2$ for all $r \not = 5$\, with $m(r\,r) \leq r-3$ when $r$ is a multiple of $4$. In this talk\, we present new upper bounds for $m(\lambda\,r)$ and examine connections between $m(5\,5)$ and several well-known conjectures for cubic graphs. \nThis is joint work with Davide Mattiolo\, Eckhard Steffen\, and Isaak H. Wolf.
URL:https://dimag.ibs.re.kr/event/2024-12-03/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20241213T163000
DTEND;TZID=Asia/Seoul:20241213T173000
DTSTAMP:20260416T073211
CREATED:20241115T050831Z
LAST-MODIFIED:20241116T074247Z
UID:10175-1734107400-1734111000@dimag.ibs.re.kr
SUMMARY:Jun Gao (高峻)\, Phase transition of degenerate Turán problems in p-norms
DESCRIPTION:For a positive real number $p$\, the $p$-norm $\|G\|_p$ of a graph $G$ is the sum of the $p$-th powers of all vertex degrees. We study the maximum $p$-norm $\mathrm{ex}_{p}(n\,F)$ of $F$-free graphs on $n$ vertices\, focusing on the case where $F$ is a bipartite graph. It is natural to conjecture that for every bipartite graph $F$\, there exists a threshold $p_F$ such that for $p< p_{F}$\, the order of $\mathrm{ex}_{p}(n\,F)$ is governed by pseudorandom constructions\, while for $p > p_{F}$\, it is governed by star-like constructions. We determine the exact value of $p_{F}$\, under a mild assumption on the growth rate of $\mathrm{ex}(n\,F)$. Our results extend to $r$-uniform hypergraphs as well. \nWe also prove a general upper bound that is tight up to a $\log n$ factor for $\mathrm{ex}_{p}(n\,F)$ when $p = p_{F}$.\nWe conjecture that this $\log n$ factor is unnecessary and prove this conjecture for several classes of well-studied bipartite graphs\, including one-side degree-bounded graphs and families of short even cycles. \nThis is a joint work with Xizhi Liu\, Jie Ma and Oleg Pikhurko.
URL:https://dimag.ibs.re.kr/event/2024-12-13/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20241217T163000
DTEND;TZID=Asia/Seoul:20241217T173000
DTSTAMP:20260416T073211
CREATED:20241115T062835Z
LAST-MODIFIED:20241115T064748Z
UID:10177-1734453000-1734456600@dimag.ibs.re.kr
SUMMARY:Joonkyung Lee (이준경)\, Counting homomorphisms in antiferromagnetic graphs via Lorentzian polynomials
DESCRIPTION:An edge-weighted graph $G$\, possibly with loops\, is said to be antiferromagnetic if it has nonnegative weights and at most one positive eigenvalue\, counting multiplicities. The number of graph homomorphisms from a graph $H$ to an antiferromagnetic graph $G$ generalises various important parameters in graph theory\, including the number of independent sets and proper vertex colourings. \nWe obtain a number of new homomorphism inequalities for antiferromagnetic target graphs $G$. In particular\, we prove that\, for any antiferromagnetic $G$\, \n$|\mathrm{Hom}(K_d\, G)|^{1/d} ≤ |\mathrm{Hom}(K_{d\,d} \setminus M\, G)|^{1/(2d)}$ \nholds\, where $K_{d\,d} \setminus M$ denotes the complete bipartite graph $K_{d\,d}$ minus a perfect matching $M$. This confirms a conjecture of Sah\, Sawhney\, Stoner and Zhao for complete graphs $K_d$. Our method uses the emerging theory of Lorentzian polynomials due to Brändén and Huh\, which may be of independent interest. \nJoint work with Jaeseong Oh and Jaehyeon Seo.
URL:https://dimag.ibs.re.kr/event/2024-12-17/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20241223T163000
DTEND;TZID=Asia/Seoul:20241223T173000
DTSTAMP:20260416T073211
CREATED:20241115T065846Z
LAST-MODIFIED:20241214T083034Z
UID:10184-1734971400-1734975000@dimag.ibs.re.kr
SUMMARY:Zixiang Xu (徐子翔)\, Multilinear polynomial methods and stability results on set systems
DESCRIPTION:In 1966\, Kleitman established that if \( |A \triangle B| \leq d \) for any \( A\, B \in \mathcal{F} \)\, then \( |\mathcal{F}| \leq \sum_{i=0}^{k} \binom{n}{i} \) for \( d = 2k \)\, and \( |\mathcal{F}| \leq 2 \sum_{i=0}^{k} \binom{n-1}{i} \) for \( d = 2k+1 \). These upper bounds are attained by the radius-\(k\) Hamming ball \( \mathcal{K}(n\, k) := \{ F : F \subseteq [n]\, |F| \leq k \} \) in the even case\, and by the family \( \mathcal{K}_y(n\, k) := \{ F : F \subseteq [n]\, |F \setminus \{y\}| \leq k \} \) in the odd case. In 2017\, Frankl provided a combinatorial proof of a stability result for Kleitman’s theorem\, offering improved upper bounds for \( |\mathcal{F}| \) when \( \mathcal{F} \) is not the extremal structure. \nIn this talk\, I will begin by demonstrating the application of multilinear polynomial methods in extremal set theory\, highlighting some interesting techniques. I will then present an algebraic proof of the stability result for Kleitman’s theorem. Finally\, I will discuss further applications and explore how to employ linear algebra methods more effectively and flexibly. \nThis talk is based on joint work with Jun Gao and Hong Liu.
URL:https://dimag.ibs.re.kr/event/2024-12-23/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20250103T163000
DTEND;TZID=Asia/Seoul:20250103T173000
DTSTAMP:20260416T073211
CREATED:20241119T145133Z
LAST-MODIFIED:20241204T064732Z
UID:10203-1735921800-1735925400@dimag.ibs.re.kr
SUMMARY:Huy Tuan Pham\, Random Cayley graphs and Additive combinatorics without groups
DESCRIPTION:A major goal of additive combinatorics is to understand the structures of subsets A of an abelian group G which has a small doubling K = |A+A|/|A|. Freiman’s celebrated theorem first provided a structural characterization of sets with small doubling over the integers\, and subsequently Ruzsa in 1999 proved an analog for abelian groups with bounded exponent. Ruzsa further conjectured the correct quantitative dependence on the doubling K in his structural result\, which has attracted several interesting developments over the next two decades. I will discuss a complete resolution of (a strengthening of) Ruzsa’s conjecture. \nSurprisingly\, our approach is crucially motivated by purely graph-theoretic insights\, where we find that the group structure is superfluous and can be replaced by much more general combinatorial structures. Using this general approach\, we also obtain combinatorial and nonabelian generalizations of classical results in additive combinatorics\, and solve longstanding open problems around Cayley graphs and random Cayley graphs motivated by Ramsey theory\, information theory and computer science. \nBased on joint work with David Conlon\, Jacob Fox and Liana Yepremyan.
URL:https://dimag.ibs.re.kr/event/2025-01-03/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20250114T163000
DTEND;TZID=Asia/Seoul:20250114T173000
DTSTAMP:20260416T073211
CREATED:20241226T072931Z
LAST-MODIFIED:20241230T145546Z
UID:10322-1736872200-1736875800@dimag.ibs.re.kr
SUMMARY:Tony Huynh\, The Peaceable Queens Problem
DESCRIPTION:The peaceable queens problem asks to determine the maximum number $a(n)$ such that there is a placement of $a(n)$ white queens and $a(n)$ black queens on an $n \times n$ chessboard so that no queen can capture any queen of the opposite color. \nWe consider the peaceable queens problem and its variant on the toroidal board.  For the regular board\, we show that $a(n) \leq 0.1716n^2$\, for all sufficiently large $n$.  This improves on the bound $a(n) \leq 0.25n^2$ of van Bommel and MacEachern. \nFor the toroidal board\, we provide new upper and lower bounds.  Somewhat surprisingly\, our bounds show that there is a sharp contrast in behaviour between the odd torus and the even torus.  Our lower bounds are given by explicit constructions.  For the upper bounds\, we formulate the problem as a non-linear optimization problem with at most 100 variables\, regardless of the size of the board. We solve our non-linear program exactly using modern optimization software. \nWe also provide a local search algorithm and a software implementation which converges very rapidly to solutions which appear optimal.  Our algorithm is sufficiently robust that it works on both the regular and toroidal boards.  For example\, for the regular board\, the algorithm quickly finds the so-called Ainley construction. \nThis is joint work with Katie Clinch\, Matthew Drescher\, and Abdallah Saffidine.
URL:https://dimag.ibs.re.kr/event/2025-01-14/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20250121T163000
DTEND;TZID=Asia/Seoul:20250121T173000
DTSTAMP:20260416T073211
CREATED:20241213T151545Z
LAST-MODIFIED:20241213T151545Z
UID:10270-1737477000-1737480600@dimag.ibs.re.kr
SUMMARY:Laure Morelle\, Bounded size modifications in time $2^{{\sf poly}(k)}\cdot n^2$
DESCRIPTION:A replacement action is a function $\mathcal L$ that maps each graph to a collection of subgraphs of smaller size. \nGiven a graph class $\mathcal H$\, we consider a general family of graph modification problems\, called “$\mathcal L$-Replacement to $\mathcal H$”\, where the input is a graph $G$ and the question is whether it is possible to replace some induced subgraph $H_1$ of $G$ on at most $k$ vertices by a graph $H_2$ in ${\mathcal L}(H_1)$ so that the resulting graph belongs to $\mathcal H$. \n“$\mathcal L$-Replacement to $\mathcal H$” can simulate many graph modification problems including vertex deletion\, edge deletion/addition/edition/contraction\, vertex identification\, subgraph complementation\, independent set deletion\, (induced) matching deletion/contraction\, etc. \nWe prove here that\, for any minor-closed graph class $\mathcal H$ and for any action $\mathcal L$ that is hereditary\, there is an algorithm that solves “$\mathcal L$-Replacement to $\mathcal H$” in time $2^{{\sf poly}(k)}\cdot |V(G)|^2$\, where $\sf poly$ is a polynomial whose degree depends on $\mathcal H$.
URL:https://dimag.ibs.re.kr/event/2025-01-21/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;VALUE=DATE:20250203
DTEND;VALUE=DATE:20250206
DTSTAMP:20260416T073211
CREATED:20250121T050727Z
LAST-MODIFIED:20250121T050727Z
UID:10456-1738540800-1738799999@dimag.ibs.re.kr
SUMMARY:IBS-DIMAG Winter School on Graph Minors\, Week 1
DESCRIPTION:
URL:https://dimag.ibs.re.kr/event/graph-minors-week-1/
LOCATION:Room B109\, IBS (기초과학연구원)
CATEGORIES:Workshops and Conferences
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20250204T163000
DTEND;TZID=Asia/Seoul:20250204T173000
DTSTAMP:20260416T073211
CREATED:20241226T073135Z
LAST-MODIFIED:20241230T024913Z
UID:10324-1738686600-1738690200@dimag.ibs.re.kr
SUMMARY:Jang Soo Kim (김장수)\, Longest elements in a semigroup of functions and Slater indices
DESCRIPTION:The group \( S_n \) of permutations on \([n]=\{1\,2\,\dots\,n\} \) is generated by simple transpositions \( s_i = (i\,i+1) \). The length \( \ell(\pi) \) of a permutation \( \pi \) is defined to be the minimum number of generators whose product is \( \pi \). It is well-known that the longest element in \( S_n \) has length \( n(n-1)/2 \). Let \( F_n \) be the semigroup of functions \( f:[n]\to[n] \)\, which are generated by the simple transpositions \( s_i \) and the function \( t:[n]\to[n] \) given by \( t(1) =t(2) = 1 \) and \( t(i) = i \) for \( i\ge3 \). The length \( \ell(f) \) of a function \( f\in F_n \) is defined to be the minimum number of these generators whose product is \( f \). In this talk\, we study the length of longest elements in \( F_n \). We also find a connection with the Slater index of a tournament of the\ncomplete graph \( K_n \). This is joint work with Yasuhide Numata.
URL:https://dimag.ibs.re.kr/event/2025-02-04/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;VALUE=DATE:20250210
DTEND;VALUE=DATE:20250213
DTSTAMP:20260416T073211
CREATED:20250121T050854Z
LAST-MODIFIED:20250121T050854Z
UID:10460-1739145600-1739404799@dimag.ibs.re.kr
SUMMARY:IBS-DIMAG Winter School on Graph Minors\, Week 2
DESCRIPTION:
URL:https://dimag.ibs.re.kr/event/graph-minors-week-2/
LOCATION:Room B109\, IBS (기초과학연구원)
CATEGORIES:Workshops and Conferences
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20250211T163000
DTEND;TZID=Asia/Seoul:20250211T173000
DTSTAMP:20260416T073211
CREATED:20241226T073216Z
LAST-MODIFIED:20250119T115501Z
UID:10327-1739291400-1739295000@dimag.ibs.re.kr
SUMMARY:Jungho Ahn (안정호)\, A coarse Erdős-Pósa theorem for constrained cycles
DESCRIPTION:An induced packing of cycles in a graph is a set of vertex-disjoint cycles such that the graph has no edge between distinct cycles of the set. The classic Erdős-Pósa theorem shows that for every positive integer $k$\, every graph contains $k$ vertex-disjoint cycles or a set of $O(k\log k)$ vertices which intersects every cycle of $G$. \nWe generalise this classic Erdős-Pósa theorem to induced packings of cycles of length at least $\ell$ for any integer $\ell$. We show that there exists a function $f(k\,\ell)=O(\ell k\log k)$ such that for all positive integers $k$ and $\ell$ with $\ell\geq3$\, every graph $G$ contains an induced packing of $k$ cycles of length at least $\ell$ or a set $X$ of at most $f(k\,\ell)$ vertices such that the closed neighbourhood of $X$ intersects every cycle of $G$. \nFurthermore\, we extend the result to long cycles containing prescribed vertices. For a graph $G$ and a set $S\subseteq V(G)$\, an $S$-cycle in $G$ is a cycle containing a vertex in $S$. We show that for all positive integers $k$ and $\ell$ with $\ell\geq3$\, every graph $G$\, and every set $S\subseteq V(G)$\, $G$ contains an induced packing of $k$ $S$-cycles of length at least $\ell$ or a set $X$ of at most $\ell k^{O(1)}$ vertices such that the closed neighbourhood of $X$ intersects every cycle of $G$. \nOur proofs are constructive and yield polynomial-time algorithms\, for fixed $\ell$\, finding either the induced packing of the constrained cycles or the set $X$. \nThis is based on joint works with Pascal Gollin\, Tony Huynh\, and O-joung Kwon.
URL:https://dimag.ibs.re.kr/event/2025-02-11/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;VALUE=DATE:20250217
DTEND;VALUE=DATE:20250220
DTSTAMP:20260416T073211
CREATED:20250121T051001Z
LAST-MODIFIED:20250121T051001Z
UID:10462-1739750400-1740009599@dimag.ibs.re.kr
SUMMARY:IBS-DIMAG Winter School on Graph Minors\, Week 3
DESCRIPTION:
URL:https://dimag.ibs.re.kr/event/graph-minors-week-3/
LOCATION:Room B109\, IBS (기초과학연구원)
CATEGORIES:Workshops and Conferences
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20250218T163000
DTEND;TZID=Asia/Seoul:20250218T173000
DTSTAMP:20260416T073211
CREATED:20250123T111843Z
LAST-MODIFIED:20250123T111843Z
UID:10488-1739896200-1739899800@dimag.ibs.re.kr
SUMMARY:O-joung Kwon (권오정)\, Erdős-Pósa property of A-paths in unoriented group-labelled graphs
DESCRIPTION:A family $\mathcal{F}$ of graphs is said to satisfy the Erdős-Pósa property if there exists a function $f$ such that for every positive integer $k$\, every graph $G$ contains either $k$ (vertex-)disjoint subgraphs in $\mathcal{F}$ or a set of at most $f(k)$ vertices intersecting every subgraph of $G$ in $\mathcal{F}$. We characterize the obstructions to the Erdős-Pósa property of $A$-paths in unoriented group-labelled graphs. As a result\, we prove that for every finite abelian group $\Gamma$ and for every subset $\Lambda$ of $\Gamma$\, the family of $\Gamma$-labelled $A$-paths whose lengths are in $\Lambda$ satisfies the half-integral relaxation of the Erdős-Pósa property. Moreover\, we give a characterization of such $\Gamma$ and $\Lambda\subseteq\Gamma$ for which the same family of $A$-paths satisfies the full Erdős-Pósa property. This is joint work with Youngho Yoo.
URL:https://dimag.ibs.re.kr/event/2025-02-18/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20250225T163000
DTEND;TZID=Asia/Seoul:20250225T173000
DTSTAMP:20260416T073211
CREATED:20250104T011404Z
LAST-MODIFIED:20250214T002236Z
UID:10354-1740501000-1740504600@dimag.ibs.re.kr
SUMMARY:Sepehr Hajebi\, The pathwidth theorem for induced subgraphs
DESCRIPTION:We present a full characterization of the unavoidable induced subgraphs of graphs with large pathwidth. This consists of two results. The first result says that for every forest H\, every graph of sufficiently large pathwidth contains either a large complete subgraph\, a large complete bipartite induced minor\, or an induced minor isomorphic to H. The second result describes the unavoidable induced subgraphs of graphs with a large complete bipartite induced minor. \nWe will also try to discuss the proof of the first result with as much detail as time permits. \nBased on joint work with Maria Chudnovsky and Sophie Spirkl.
URL:https://dimag.ibs.re.kr/event/2025-02-25/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20250304T163000
DTEND;TZID=Asia/Seoul:20250304T173000
DTSTAMP:20260416T073211
CREATED:20250123T112518Z
LAST-MODIFIED:20250223T142525Z
UID:10492-1741105800-1741109400@dimag.ibs.re.kr
SUMMARY:Irene Muzi\, An elementary bound for Younger's conjecture
DESCRIPTION:In 1996\, Reed\, Robertson\, Seymour and Thomas proved Younger’s Conjecture\, which states that for all directed graphs D\, there exists a function f such that if D does not contain k disjoint cycles\, D contains a feedback vertex set\, i.e. a subset of vertices whose deletion renders the graph acyclic\, of size bounded by f(k). However\, the function obtained by Reed\, Robertson\, Seymour and Thomas is enormous and\, in fact\, not even elementary. The bound had\, so far\, not been improved. In this talk\, I will present new techniques to improve the bound from non-elementary to elementary. This is joint work with Meike Hatzel\, Stephan Kreutzer and Marcelo Milani.
URL:https://dimag.ibs.re.kr/event/2025-03-04/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20250311T163000
DTEND;TZID=Asia/Seoul:20250311T173000
DTSTAMP:20260416T073211
CREATED:20240909T194937Z
LAST-MODIFIED:20250218T150344Z
UID:9870-1741710600-1741714200@dimag.ibs.re.kr
SUMMARY:Johannes Carmesin\, Open problems in graph theory
DESCRIPTION:Since the proof of the graph minor structure theorem by Robertson and Seymour in 2004\, its underlying ideas have found applications in a much broader range of settings than their original context. They have driven profound progress in areas such as vertex minors\, pivot minors\, matroids\, directed graphs\, and 2-dimensional simplicial complexes. In this talk\, I will present three open problems related to this development\, each requiring some background.
URL:https://dimag.ibs.re.kr/event/2025-03-11/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20250318T163000
DTEND;TZID=Asia/Seoul:20250318T173000
DTSTAMP:20260416T073211
CREATED:20250205T073256Z
LAST-MODIFIED:20250305T204931Z
UID:10539-1742315400-1742319000@dimag.ibs.re.kr
SUMMARY:Michał Seweryn\, Dimension and standard examples in planar posets
DESCRIPTION:The dimension of a poset is the least integer $d$ such that the poset is isomorphic to a subposet of the product of $d$ linear orders. In 1983\, Kelly constructed planar posets of arbitrarily large dimension. Crucially\, the posets in his construction involve large standard examples\, the canonical structure preventing a poset from having small dimension. Kelly’s construction inspired one of the most challenging questions in dimension theory: are large standard examples unavoidable in planar posets of large dimension? We answer the question affirmatively by proving that every $d$-dimensional planar poset contains a standard example of order $\Omega(d)$. More generally\, we prove that every poset from Kelly’s construction appears in every poset with a planar cover graph of sufficiently large dimension. \njoint work with Heather Smith Blake\, Jędrzej Hodor\, Piotr Micek\, and William T. Trotter.
URL:https://dimag.ibs.re.kr/event/2025-03-18/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20250401T163000
DTEND;TZID=Asia/Seoul:20250401T173000
DTSTAMP:20260416T073211
CREATED:20250310T023035Z
LAST-MODIFIED:20250310T023155Z
UID:10673-1743525000-1743528600@dimag.ibs.re.kr
SUMMARY:Hyunwoo Lee (이현우)\, Reconstructing hypergraph matching polynomials
DESCRIPTION:By utilizing the recently developed hypergraph analogue of Godsil’s identity by the second author\, we prove that for all $n \geq k \geq 2$\, one can reconstruct the matching polynomial of an $n$-vertex $k$-uniform hypergraph from the multiset of all induced sub-hypergraphs on $\lfloor \frac{k-1}{k}n \rfloor + 1$ vertices. This generalizes the well-known result of Godsil on graphs in 1981 to every uniform hypergraph. As a corollary\, we show that for every graph $F$\, one can reconstruct the number of $F$-factors in a graph under analogous conditions. We also constructed examples that imply the number $\lfloor \frac{k-1}{k}n \rfloor + 1$ is the best possible for all $n\geq k \geq 2$ with $n$ divisible by $k$. This is joint work Donggyu Kim.
URL:https://dimag.ibs.re.kr/event/2025-04-01/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20250408T163000
DTEND;TZID=Asia/Seoul:20250408T173000
DTSTAMP:20260416T073211
CREATED:20250210T063056Z
LAST-MODIFIED:20250331T224202Z
UID:10560-1744129800-1744133400@dimag.ibs.re.kr
SUMMARY:Marcelo Garlet Milani\, Cycles of Well-Linked Sets and an Elementary Bound for the Directed Grid Theorem
DESCRIPTION:In 2015\, Kawarabayashi and Kreutzer proved the directed grid theorem. The theorem states the existence of a function f such that every digraph of directed tree-width f(k) contains a cylindrical grid of order k as a butterfly minor\, but the given function grows non-elementarily with the size of the grid minor. \nWe present an alternative proof of the directed grid theorem\, first proven by Kawarabayashi and Kreutzer in 2015\, which is conceptually much simpler\, more modular in its composition and also improves the upper bound for the function f to a power tower of height 22. \nOur proof is inspired by the breakthrough result of Chekuri and Chuzhoy\, who proved a polynomial bound for the excluded grid theorem for undirected graphs. We translate a key concept of their proof to directed graphs by introducing cycles of well-linked sets (CWS)\, and show that any digraph of high directed tree-width contains a large CWS\, which in turn contains a large cylindrical grid. \nThis is joint work with Meike Hatzel\, Stephan Kreutzer and Irene Muzi.
URL:https://dimag.ibs.re.kr/event/2025-04-08/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20250414T110000
DTEND;TZID=Asia/Seoul:20250414T120000
DTSTAMP:20260416T073211
CREATED:20250218T063907Z
LAST-MODIFIED:20250318T144436Z
UID:10608-1744628400-1744632000@dimag.ibs.re.kr
SUMMARY:Daniel McGinnis\, A necessary and sufficient condition for $k$-transversals
DESCRIPTION:We solve a long-standing open problem posed by Goodman and Pollack in 1988 by establishing a necessary and sufficient condition for a finite family of convex sets in $\mathbb{R}^d$ to admit a $k$-transversal (a $k$-dimensional affine subspace that intersects each set) for any $0 \le k \le d-1$. This result is a common generalization of Helly’s theorem ($k=0$) and the Goodman-Pollack-Wenger theorem ($k=d-1$). \nThis is joint work with Nikola Sadovek.
URL:https://dimag.ibs.re.kr/event/2025-04-14/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20250415T163000
DTEND;TZID=Asia/Seoul:20250415T173000
DTSTAMP:20260416T073211
CREATED:20250211T042237Z
LAST-MODIFIED:20250331T222415Z
UID:10569-1744734600-1744738200@dimag.ibs.re.kr
SUMMARY:Nicola Lorenz\, A Minor Characterisation of Normally Spanned Sets of Vertices
DESCRIPTION:A rooted spanning tree of a graph $G$ is called normal if the endvertices of all edges of $G$ are comparable in the tree order. It is well known that every finite connected graph has a normal spanning tree (also known as depth-first search tree). Also\, all countable graphs have normal spanning trees\, but uncountable complete graphs for example do not. In 2021\, Pitz proved the following characterisation for graphs with normal spanning trees\, which had been conjectured by Halin: A connected graph $G$ has a normal spanning tree if and only if every minor of $G$ has countable colouring number\, i.e. there is a well-order of the vertices such that every vertex is preceded by only finitely many of its neighbours. \nMore generally\, a not necessarily spanning tree in $G$ is called normal if for every path $P$ in $G$ with both endvertices in $T$ but no inner vertices in $T$\, the endvertices of $P$ are comparable in the tree order. We establish a local version of Pitz’s theorem by characterising for which sets $U$ of vertices of $G$ there is a normal tree in $G$ covering $U$. The results are joint work with Max Pitz.
URL:https://dimag.ibs.re.kr/event/2025-04-15/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20250422T163000
DTEND;TZID=Asia/Seoul:20250422T173000
DTSTAMP:20260416T073211
CREATED:20250210T062933Z
LAST-MODIFIED:20250414T092141Z
UID:10558-1745339400-1745343000@dimag.ibs.re.kr
SUMMARY:Marcin Briański\, Burling Graphs as (almost) universal obstacles to  $\chi$-boundedness
DESCRIPTION:What causes a graph to have high chromatic number? One obvious reason is containing a large clique (a set of pairwise adjacent vertices). This naturally leads to investigation of \(\chi\)-bounded classes of graphs — classes where a large clique is essentially the only reason for large chromatic number. \nUnfortunately\, many interesting graph classes are not \(\chi\)-bounded. An eerily common obstruction to being \(\chi\)-bounded are the Burling graphs — a family of triangle-free graphs with unbounded chromatic number. These graphs have served as counterexamples in many settings: demonstrating that graphs excluding an induced subdivision of \(K_{5}\) are not \(\chi\)-bounded\, that string graphs are not \(\chi\)-bounded\, that intersection graphs of boxes in \({\mathbb{R}}^{3}\) are not \(\chi\)-bounded\, and many others. \nIn many of these cases\, this sequence is the only known obstruction to \(\chi\)-boundedness. This led Chudnovsky\, Scott\, and Seymour to conjecture that any graph of sufficiently high chromatic number must either contain a large clique\, an induced proper subdivision of a clique\, or a large Burling graph as an induced subgraph. \nThe prevailing belief was that this conjecture should be false. Somewhat surprisingly\, we did manage to prove it under an extra assumption on the “locality” of the chromatic number — that the input graph belongs to a \(2\)-controlled family of graphs\, where a high chromatic number is always certified by a ball of radius \(2\) with large chromatic number. \nIn this talk\, I will present this result and discuss its implications in structural graph theory\, and algorithmic implications to colouring problems in specific graph families. \nThis talk is based on joint work with Tara Abrishami\, James Davies\, Xiying Du\, Jana Masaříková\, Paweł Rzążewski\, and Bartosz Walczak conducted during the STWOR2 workshop in Chęciny Poland.
URL:https://dimag.ibs.re.kr/event/2025-04-22/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
END:VCALENDAR