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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
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BEGIN:VTIMEZONE
TZID:Asia/Seoul
BEGIN:STANDARD
TZOFFSETFROM:+0900
TZOFFSETTO:+0900
TZNAME:KST
DTSTART:20220101T000000
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230718T163000
DTEND;TZID=Asia/Seoul:20230718T173000
DTSTAMP:20260416T191942
CREATED:20230601T142456Z
LAST-MODIFIED:20240705T163017Z
UID:7226-1689697800-1689701400@dimag.ibs.re.kr
SUMMARY:Andrzej Grzesik\, Rainbow Turán problems
DESCRIPTION:In a rainbow variant of the Turán problem\, we consider $k$ graphs on the same set of vertices and want to determine the smallest possible number of edges in each graph\, which guarantees the existence of a copy of a given graph $F$ containing at most one edge from each graph. In other words\, we treat each of the $k$ graphs as a graph in one of the $k$ colors and consider how many edges in each color force a rainbow copy of a given graph $F$. In the talk\, we will describe known results on the topic\, as well as present recent developments\, obtained jointly with Sebastian Babiński and Magdalen Prorok\, solving the rainbow Turán problem for a path on 4 vertices and a directed triangle with any number of colors.
URL:https://dimag.ibs.re.kr/event/2023-07-18/
LOCATION:Room S221\, IBS (기초과학연구원) Science Culture Center
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230713T094000
DTEND;TZID=Asia/Seoul:20230713T105000
DTSTAMP:20260416T191942
CREATED:20230711T000049Z
LAST-MODIFIED:20240705T162121Z
UID:7377-1689241200-1689245400@dimag.ibs.re.kr
SUMMARY:Open Symposium at the Discrete Mathematics Group
DESCRIPTION:Program\n\n9:40-10:05: Sang-il OUM\, Obstructions for dense analogs of tree-depth\n10:05-10:20: Kevin HENDREY\, Structural and extremal results for twin-width\n10:20-10:35: Rutger CAMPBELL\, Down-sets in combinatorial posets\n10:35-10:50: Linda COOK\, Reuniting 𝜒-boundedness with polynomial 𝜒-boundedness
URL:https://dimag.ibs.re.kr/event/2023-07-11/
LOCATION:Room B109\, IBS (기초과학연구원)
CATEGORIES:Workshops and Conferences
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230710T163000
DTEND;TZID=Asia/Seoul:20230710T173000
DTSTAMP:20260416T191942
CREATED:20230410T004309Z
LAST-MODIFIED:20240707T073602Z
UID:6987-1689006600-1689010200@dimag.ibs.re.kr
SUMMARY:Xuding Zhu (朱緒鼎)\, List version of 1-2-3 conjecture
DESCRIPTION:The well-known 1-2-3 Conjecture by Karoński\, Łuczak and Thomason states that the edges of any connected graph with at least three vertices can be assigned weights 1\, 2 or 3 so that for each edge $uv$ the sums of the weights at $u$ and at $v$ are distinct. The list version of the 1-2-3 Conjecture by Bartnicki\, Grytczuk and Niwczyk states that the same holds if each edge $e$ has the choice of weights not necessarily from $\{1\,2\,3\}$\, but from any set $\{x(e)\,y(e)\,z(e)\}$ of three real numbers. The goal of this talk is to survey developments on the 1-2-3 Conjecture\, especially on the list version of the 1-2-3 Conjecture.
URL:https://dimag.ibs.re.kr/event/2023-07-10/
LOCATION:Room B109\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230704T163000
DTEND;TZID=Asia/Seoul:20230704T173000
DTSTAMP:20260416T191942
CREATED:20230627T045021Z
LAST-MODIFIED:20240705T162129Z
UID:7316-1688488200-1688491800@dimag.ibs.re.kr
SUMMARY:Tuan Tran\, Complexity of null dynamical systems
DESCRIPTION:A theoretical dynamical system is a pair (X\,T) where X is a compact metric space and T is a self homeomorphism of X. The topological entropy of a theoretical dynamical system (X\,T)\, first introduced in 1965 by Adler\, Konheim and McAndrew\, is a nonnegative real number that measures the complexity of the system. Systems with positive entropy are random in certain sense\, and systems with zero entropy are said to be deterministic. To distinguish between deterministic systems\, Huang and Ye (2009) introduced the concept of maximal pattern entropy of a theoretical dynamical system. At the heart of their argument is a Sauer-Shelah-type lemma. We will discuss this lemma and its surprising connection to a recent breakthrough in communication complexity. \nJoint work with Guorong Gao\, Jie Ma\, and Mingyuan Rong.
URL:https://dimag.ibs.re.kr/event/2023-07-04/
LOCATION:Room B109\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230627T163000
DTEND;TZID=Asia/Seoul:20230627T173000
DTSTAMP:20260416T191942
CREATED:20230601T063015Z
LAST-MODIFIED:20240707T073615Z
UID:7223-1687883400-1687887000@dimag.ibs.re.kr
SUMMARY:Chong Shangguan (上官冲)\, The hat guessing number of graphs
DESCRIPTION:Consider the following hat guessing game: $n$ players are placed on $n$ vertices of a graph\, each wearing a hat whose color is arbitrarily chosen from a set of $q$ possible colors. Each player can see the hat colors of his neighbors\, but not his own hat color. All of the players are asked to guess their own hat colors simultaneously\, according to a predetermined guessing strategy and the hat colors they see\, where no communication between them is allowed. Given a graph $G$\, its hat guessing number $HG(G)$ is the largest integer $q$ such that there exists a guessing strategy guaranteeing at least one correct guess for any hat assignment of $q$ possible colors. \nIn 2008\, Butler\, Hajiaghayi\, Kleinberg\, and Leighton asked whether the hat guessing number of the complete bipartite graph $K_{n\,n}$ is at least some fixed positive (fractional) power of $n$. We answer this question affirmatively\, showing that for sufficiently large $n$\, $HG(K_{n\,n})\ge n^{0.5-o(1)}$. Our guessing strategy is based on some ideas from coding theory and probabilistic method. \nBased on a joint work with Noga Alon\, Omri Ben-Eliezer\, and Itzhak Tamo.
URL:https://dimag.ibs.re.kr/event/2023-06-27/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230620T163000
DTEND;TZID=Asia/Seoul:20230620T173000
DTSTAMP:20260416T191942
CREATED:20230410T120415Z
LAST-MODIFIED:20240705T164137Z
UID:6995-1687278600-1687282200@dimag.ibs.re.kr
SUMMARY:Guanghui Wang (王光辉)\, Embeddings in uniformly dense  hypergraphs
DESCRIPTION:An archetype problem in extremal combinatorics is to study the structure of subgraphs appearing in different classes of (hyper)graphs. We will focus on such embedding problems in uniformly dense hypergraphs. In precise\, we will mention the uniform Turan density of some hypergraphs.
URL:https://dimag.ibs.re.kr/event/2023-06-23/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230613T163000
DTEND;TZID=Asia/Seoul:20230613T173000
DTSTAMP:20260416T191942
CREATED:20230410T043558Z
LAST-MODIFIED:20240707T073632Z
UID:6992-1686673800-1686677400@dimag.ibs.re.kr
SUMMARY:Minho Cho (조민호)\, Strong Erdős-Hajnal property on chordal graphs and its variants
DESCRIPTION:A graph class $\mathcal{G}$ has the strong Erdős-Hajnal property (SEH-property) if there is a constant $c=c(\mathcal{G}) > 0$ such that for every member $G$ of $\mathcal{G}$\, either $G$ or its complement has $K_{m\, m}$ as a subgraph where $m \geq \left\lfloor c|V(G)| \right\rfloor$. We prove that the class of chordal graphs satisfies SEH-property with constant $c = 2/9$. \nOn the other hand\, a strengthening of SEH-property which we call the colorful Erdős-Hajnal property was discussed in geometric settings by Alon et al.(2005) and by Fox et al.(2012). Inspired by their results\, we show that for every pair $F_1\, F_2$ of subtree families of the same size in a tree $T$ with $k$ leaves\, there exist subfamilies $F’_1 \subseteq F_1$ and $F’_2 \subseteq F_2$ of size $\theta \left( \frac{\ln k}{k} \left| F_1 \right|\right)$ such that either every pair of representatives from distinct subfamilies intersect or every such pair do not intersect. Our results are asymptotically optimal. \nJoint work with Andreas Holmsen\, Jinha Kim and Minki Kim.
URL:https://dimag.ibs.re.kr/event/2023-06-13/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230530T163000
DTEND;TZID=Asia/Seoul:20230530T173000
DTSTAMP:20260416T191942
CREATED:20230323T234815Z
LAST-MODIFIED:20240707T073642Z
UID:6946-1685464200-1685467800@dimag.ibs.re.kr
SUMMARY:Suyun Jiang (江素云)\, How connectivity affects the extremal number of trees
DESCRIPTION:The Erdős-Sós conjecture states that the maximum number of edges in an $n$-vertex graph without a given $k$-vertex tree is at most $\frac {n(k-2)}{2}$. Despite significant interest\, the conjecture remains unsolved. Recently\, Caro\, Patkós\, and Tuza considered this problem for host graphs that are connected. Settling a problem posed by them\, for a $k$-vertex tree $T$\, we construct $n$-vertex connected graphs that are $T$-free with at least $(1/4-o_k(1))nk$ edges\, showing that the additional connectivity condition can reduce the maximum size by at most a factor of 2. Furthermore\, we show that this is optimal: there is a family of $k$-vertex brooms $T$ such that the maximum size of an $n$-vertex connected $T$-free graph is at most $(1/4+o_k(1))nk$.
URL:https://dimag.ibs.re.kr/event/2023-05-30/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230517T160000
DTEND;TZID=Asia/Seoul:20230517T170000
DTSTAMP:20260416T191942
CREATED:20230220T090319Z
LAST-MODIFIED:20240705T165050Z
UID:6807-1684339200-1684342800@dimag.ibs.re.kr
SUMMARY:Szymon Toruńczyk\, Flip-width: Cops and Robber on dense graphs
DESCRIPTION:We define new graph parameters\, called flip-width\, that generalize treewidth\, degeneracy\, and generalized coloring numbers for sparse graphs\, and clique-width and twin-width for dense graphs. The flip-width parameters are defined using variants of the Cops and Robber game\, in which the robber has speed bounded by a fixed constant  r∈N∪{∞}\, and the cops perform flips (or perturbations) of the considered graph. We then propose a new notion of tameness of a graph class\, called bounded flip-width\, which is a dense counterpart of classes of bounded expansion of Nešetril and Ossona de Mendez\, and includes classes of bounded twin-width of Bonnet\, Kim\, Thomassé\, and Watrigant. This unifies Sparsity Theory and Twin-width Theory\, providing a common language for studying the central notions of the two theories\, such as weak coloring numbers and twin-width — corresponding to winning strategies of one player — or dense shallow minors\, rich divisions\, or well-linked sets\, corresponding to winning strategies of the other player. We prove that boundedness of flip-width is preserved by first-order interpretations\, or transductions\, generalizing previous results concerning classes of bounded expansion and bounded twin-width. We provide an algorithm approximating the flip-width of a given graph\, which runs in slicewise polynomial time (XP) in the size of the graph. Finally\, we propose a more general notion of tameness\, called almost bounded flip-width\, which is a dense counterpart of nowhere dense classes. We conjecture\, and provide evidence\, that classes with almost bounded flip-width coincide with monadically dependent (or monadically NIP) classes\, introduced by Shelah in model theory. We also provide evidence that classes of almost bounded flip-width characterise the hereditary graph classes for which the model-checking problem is fixed-parameter tractable.
URL:https://dimag.ibs.re.kr/event/2023-05-17/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230516T163000
DTEND;TZID=Asia/Seoul:20230516T173000
DTSTAMP:20260416T191942
CREATED:20230116T010528Z
LAST-MODIFIED:20240707T073700Z
UID:6669-1684254600-1684258200@dimag.ibs.re.kr
SUMMARY:Oliver Janzer\, Small subgraphs with large average degree
DESCRIPTION:We study the fundamental problem of finding small dense subgraphs in a given graph. For a real number $s>2$\, we prove that every graph on $n$ vertices with average degree at least $d$ contains a subgraph of average degree at least $s$ on at most $nd^{-\frac{s}{s-2}}(\log d)^{O_s(1)}$ vertices. This is optimal up to the polylogarithmic factor\, and resolves a conjecture of Feige and Wagner. In addition\, we show that every graph with $n$ vertices and average degree at least $n^{1-\frac{2}{s}+\varepsilon}$ contains a subgraph of average degree at least $s$ on $O_{\varepsilon\,s}(1)$ vertices\, which is also optimal up to the constant hidden in the $O(.)$ notation\, and resolves a conjecture of Verstraëte. \nJoint work with Benny Sudakov and Istvan Tomon.
URL:https://dimag.ibs.re.kr/event/2023-05-16/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230511T161500
DTEND;TZID=Asia/Seoul:20230511T171500
DTSTAMP:20260416T191942
CREATED:20230301T130657Z
LAST-MODIFIED:20240705T165043Z
UID:6864-1683821700-1683825300@dimag.ibs.re.kr
SUMMARY:Maria Chudnovsky\, Induced subgraphs and tree decompositions
DESCRIPTION:Tree decompositions are a powerful tool in both structural graph theory and graph algorithms. Many hard problems become tractable if the input graph is known to have a tree decomposition of bounded “width”. Exhibiting a particular kind of a tree decomposition is also a useful way to describe the structure of a graph. Tree decompositions have traditionally been used in the context of forbidden graph minors; bringing them into the realm of forbidden induced subgraphs has until recently remained out of reach. Over the last couple of years we have made significant progress in this direction\, exploring both the classical notion of bounded tree-width\, and concepts of more structural flavor. This talk will survey some of these ideas and results.
URL:https://dimag.ibs.re.kr/event/2023-05-11/
LOCATION:Room 1501\, Bldg. E6-1\, KAIST
CATEGORIES:Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230509T163000
DTEND;TZID=Asia/Seoul:20230509T173000
DTSTAMP:20260416T191942
CREATED:20230413T233653Z
LAST-MODIFIED:20240707T073713Z
UID:7041-1683649800-1683653400@dimag.ibs.re.kr
SUMMARY:Jozef Skokan\, Separating the edges of a graph by a linear number of paths
DESCRIPTION:Recently\, Letzter proved that any graph of order n contains a collection P of $O(n \log^*n)$ paths with the following property: for all distinct edges e and f there exists a path in P which contains e but not f. We improve this upper bound to 19n\, thus answering a question of Katona and confirming a conjecture independently posed by Balogh\, Csaba\, Martin\, and Pluhar and by Falgas-Ravry\, Kittipassorn\, Korandi\, Letzter\, and Narayanan. \nOur proof is elementary and self-contained.
URL:https://dimag.ibs.re.kr/event/2023-05-09/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230502T163000
DTEND;TZID=Asia/Seoul:20230502T173000
DTSTAMP:20260416T191942
CREATED:20230315T140009Z
LAST-MODIFIED:20240705T164210Z
UID:6916-1683045000-1683048600@dimag.ibs.re.kr
SUMMARY:Rob Morris\, An exponential improvement for diagonal Ramsey
DESCRIPTION:The Ramsey number $R(k)$ is the minimum n such that every red-blue colouring of the edges of the complete graph on n vertices contains a monochromatic copy of $K_k$. It has been known since the work of Erdős and Szekeres in 1935\, and Erdős in 1947\, that $2^{k/2} < R(k) < 4^k$\, but in the decades since the only improvements have been by lower order terms. In this talk I will sketch the proof of a very recent result\, which improves the upper bound of Erdős and Szekeres by a (small) exponential factor. \nBased on joint work with Marcelo Campos\, Simon Griffiths and Julian Sahasrabudhe.
URL:https://dimag.ibs.re.kr/event/2023-05-02/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230427T161500
DTEND;TZID=Asia/Seoul:20230427T171500
DTSTAMP:20260416T191942
CREATED:20230321T001954Z
LAST-MODIFIED:20240705T164205Z
UID:6930-1682612100-1682615700@dimag.ibs.re.kr
SUMMARY:Rob Morris\, Ramsey theory: searching for order in chaos
DESCRIPTION:In many different areas of mathematics (such as number theory\, discrete geometry\, and combinatorics)\, one is often presented with a large “unstructured” object\, and asked to find a smaller “structured” object inside it. One of the earliest and most influential examples of this phenomenon was the theorem of Ramsey\, proved in 1930\, which states that if n = n(k) is large enough\, then in any red-blue colouring of the edges of the complete graph on n vertices\, there exists a monochromatic clique on k vertices. In this talk I will discuss some of the questions\, ideas\, and new techniques that were inspired by this theorem\, and present some recent progress on one of the central problems in the area: bounding the so-called “diagonal” Ramsey numbers. Based on joint work with Marcelo Campos\, Simon Griffiths and Julian Sahasrabudhe.
URL:https://dimag.ibs.re.kr/event/2023-04-27/
LOCATION:Room 1501\, Bldg. E6-1\, KAIST
CATEGORIES:Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230425T163000
DTEND;TZID=Asia/Seoul:20230425T173000
DTSTAMP:20260416T191942
CREATED:20230315T025543Z
LAST-MODIFIED:20240707T073739Z
UID:6905-1682440200-1682443800@dimag.ibs.re.kr
SUMMARY:Hyunwoo Lee (이현우)\, On perfect subdivision tilings
DESCRIPTION:For a given graph $H$\, we say that a graph $G$ has a perfect $H$-subdivision tiling if $G$ contains a collection of vertex-disjoint subdivisions of $H$ covering all vertices of $G.$ Let $\delta_{sub}(n\, H)$ be the smallest integer $k$ such that any $n$-vertex graph $G$ with minimum degree at least $k$ has a perfect $H$-subdivision tiling. For every graph $H$\, we asymptotically determined the value of $\delta_{sub}(n\, H)$. More precisely\, for every graph $H$ with at least one edge\, there is a constant $1 < \xi^*(H)\leq 2$ such that $\delta_{sub}(n\, H) = \left(1 - \frac{1}{\xi^*(H)} + o(1) \right)n$ if $H$ has a bipartite subdivision with two parts having different parities. Otherwise\, the threshold depends on the parity of $n$.
URL:https://dimag.ibs.re.kr/event/2023-04-25/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230419T163000
DTEND;TZID=Asia/Seoul:20230419T173000
DTSTAMP:20260416T191942
CREATED:20230301T064147Z
LAST-MODIFIED:20240705T165047Z
UID:6852-1681921800-1681925400@dimag.ibs.re.kr
SUMMARY:Shin-ichiro Seki\, On the extension of the Green-Tao theorem to number fields
DESCRIPTION:In 2006\, Tao established the Gaussian counterpart of the celebrated Green-Tao theorem on arithmetic progressions of primes. In this talk\, I will explain the extension of Tao’s theorem and the Green-Tao theorem to the case of general number fields. Our combinatorial tool is the relative hypergraph removal lemma by Conlon-Fox-Zhao. I will discuss the difficulties that arise in the case of general number fields and an application of our results to prime representations by binary quadratic forms. This is based on joint work with Wataru Kai\, Masato Mimura\, Akihiro Munemasa\, and Kiyoto Yoshino.
URL:https://dimag.ibs.re.kr/event/2023-04-19/
LOCATION:Zoom ID: 897 6822 0619 (ibsecopro) [04/19 only]
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;VALUE=DATE:20230417
DTEND;VALUE=DATE:20230425
DTSTAMP:20260416T191942
CREATED:20221108T013322Z
LAST-MODIFIED:20240705T171116Z
UID:6435-1681689600-1682380799@dimag.ibs.re.kr
SUMMARY:MATRIX-IBS Workshop: Structural Graph Theory Downunder III
DESCRIPTION:Website: https://www.matrix-inst.org.au/events/structural-graph-theory-downunder-iii/ \nProgram Description:  \nThis program\, jointly organised by MATRIX and the Discrete Mathematics Group of the Korean Institute for Basic Science (IBS)\, builds on the “Structural Graph Theory Downunder” programs held at MATRIX in 2019 and 2022. In this short intensive workshop\, mathematicians from across the globe will come together to work on open problems in structural graph theory. The focus will be on graph colouring\, graph minors\, induced subgraphs\, and graph product structure theory. The majority of the time will be allocated to collaborative research\, with only a few talks describing recent advances. The goal is to create an environment where mathematicians at all career stages work side-by-side. We anticipate that open problems will be solved\, and lasting collaborations will be initiated. \nConfirmed Participants: \nRutger Campbell (Institute for Basic Science\, Korea)\nLinda Cook (Institute for Basic Science\, Korea)\nJames Davies (University of Cambridge\, UK)\nMarc Distel (Monash University\, Australia)\nZdeněk Dvořák (Charles University\, Czech Republic)\nBryce Frederickson (Emory University\, USA)\nAntónio Girão (University of Oxford\, UK)\nPascal Gollin (Institute for Basic Science\, Korea)\nKevin Hendrey (Institute for Basic Science\, Korea)\nRobert Hickingbotham (Monash University\, Australia)\nFreddie Illingworth (University of Oxford\, UK)\nO-joung Kwon (Hanyang University\, Korea)\nFlorian Lehner (University of Auckland\, New Zealand)\nAnita Liebenau (UNSW\, Australia)\nChun-Hung Liu (Texas A&M\, USA)\nRose McCarty (Princeton University\, USA)\nLukas Michel (University of Oxford\, UK)\nSang-il Oum (Institute for Basic Science and KAIST\, Korea)\nMichael Savery (University of Oxford\, UK)\nAlex Scott (University of Oxford\, UK)\nRaphael Steiner (ETH Zurich\, Switzerland)\nJane Tan (University of Oxford\, UK)\nSebastian Wiederrecht (Institute for Basic Science\, Korea)\nDavid Wood (Monash University\, Australia)\nLiana Yepremyan (Emory University\, USA)
URL:https://dimag.ibs.re.kr/event/2023-04-17/
LOCATION:MATRIX\, Australia
CATEGORIES:Workshops and Conferences
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230411T163000
DTEND;TZID=Asia/Seoul:20230411T173000
DTSTAMP:20260416T191942
CREATED:20230220T150254Z
LAST-MODIFIED:20240705T165050Z
UID:6812-1681230600-1681234200@dimag.ibs.re.kr
SUMMARY:James Davies\, Two structural results for pivot-minors
DESCRIPTION:Pivot-minors can be thought of as a dense analogue of graph minors. We shall discuss pivot-minors and two recent results for proper pivot-minor-closed classes of graphs. In particular\, that for every graph H\, the class of graphs containing no H-pivot-minor is 𝜒-bounded\, and also satisfies the (strong) Erdős-Hajnal property.
URL:https://dimag.ibs.re.kr/event/2023-04-11/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230406T100000
DTEND;TZID=Asia/Seoul:20230406T110000
DTSTAMP:20260416T191942
CREATED:20230118T233830Z
LAST-MODIFIED:20240707T073746Z
UID:6691-1680775200-1680778800@dimag.ibs.re.kr
SUMMARY:Jie Han\, Spanning trees in expanders
DESCRIPTION:We consider the spanning tree embedding problem in dense graphs without bipartite holes and sparse graphs. In 2005\, Alon\, Krivelevich and Sudakov asked for determining the best possible spectral gap forcing an $(n\,d\,\lambda)$-graph to be $T(n\, \Delta)$-universal. In this talk\, we introduce our recent work on this conjecture.
URL:https://dimag.ibs.re.kr/event/2023-04-06/
LOCATION:Zoom ID: 224 221 2686 (ibsecopro)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230404T163000
DTEND;TZID=Asia/Seoul:20230404T173000
DTSTAMP:20260416T191942
CREATED:20230116T010354Z
LAST-MODIFIED:20240707T073814Z
UID:6667-1680625800-1680629400@dimag.ibs.re.kr
SUMMARY:István Tomon\, Configurations of boxes
DESCRIPTION:Configurations of axis-parallel boxes in $\mathbb{R}^d$ are extensively studied in combinatorial geometry. Despite their perceived simplicity\, there are many problems involving their structure that are not well understood. I will talk about a construction that shows that their structure might be more complicated than people conjectured.
URL:https://dimag.ibs.re.kr/event/2023-04-04/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230328T163000
DTEND;TZID=Asia/Seoul:20230328T173000
DTSTAMP:20260416T191942
CREATED:20230223T141945Z
LAST-MODIFIED:20240705T165050Z
UID:6831-1680021000-1680024600@dimag.ibs.re.kr
SUMMARY:Tianchi Yang\, On the maximum number of edges in k-critical graphs
DESCRIPTION:In this talk\, we will discuss the problem of determining the maximum number of edges in an n-vertex k-critical graph. A graph is considered k-critical if its chromatic number is k\, but any proper subgraph has a chromatic number less than k. The problem remains open for any integer k ≥ 4. Our presentation will showcase an improvement on previous results achieved by employing a combination of extremal graph theory and structural analysis. We will introduce a key lemma\, which may be of independent interest\, as it sheds light on the partial structure of dense k-critical graphs. This is joint work with Cong Luo and Jie Ma.
URL:https://dimag.ibs.re.kr/event/2023-03-28/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230322T163000
DTEND;TZID=Asia/Seoul:20230322T173000
DTSTAMP:20260416T191942
CREATED:20230118T233720Z
LAST-MODIFIED:20240707T092054Z
UID:6688-1679502600-1679506200@dimag.ibs.re.kr
SUMMARY:Qizhong Lin\, Two classical Ramsey-Turán numbers involving triangles
DESCRIPTION:In 1993\, Erdős\, Hajnal\, Simonovits\, Sós and Szemerédi proposed to determine the value of Ramsey-Turán density $\rho(3\,q)$ for $q\ge3$. Erdős et al. (1993) and Kim\, Kim and Liu (2019) proposed two corresponding conjectures. However\, we only know four values of this Ramsey-Turán density by Erdős et al. (1993). There is no progress on this classical Ramsey-Turán density since then. In this talk\, I will introduce two new values of this classical Ramsey-Turán density. Moreover\, the corresponding asymptotically extremal structures are weakly stable\, which answers a problem of Erdős et al. (1993) for the two cases. Joint work with Xinyu Hu.
URL:https://dimag.ibs.re.kr/event/2023-03-22/
LOCATION:Zoom ID: 224 221 2686 (ibsecopro)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230321T163000
DTEND;TZID=Asia/Seoul:20230321T173000
DTSTAMP:20260416T191942
CREATED:20230204T071556Z
LAST-MODIFIED:20240705T170008Z
UID:6762-1679416200-1679419800@dimag.ibs.re.kr
SUMMARY:Younjin Kim (김연진)\, Problems on Extremal Combinatorics
DESCRIPTION:Extremal Combinatorics studies the maximum or minimum size of finite objects (numbers\, sets\, graphs) satisfying certain properties. In this talk\, I introduce the conjectures I solved on Extremal Combinatorics\, and also introduce recent extremal problems.
URL:https://dimag.ibs.re.kr/event/2023-03-21/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230316T100000
DTEND;TZID=Asia/Seoul:20230316T110000
DTSTAMP:20260416T191942
CREATED:20230213T121859Z
LAST-MODIFIED:20240707T073949Z
UID:6788-1678960800-1678964400@dimag.ibs.re.kr
SUMMARY:Paul Seymour\, A loglog step towards the Erdős-Hajnal conjecture
DESCRIPTION:In 1977\, Erdős and Hajnal made the conjecture that\, for every graph $H$\, there exists $c>0$ such that every $H$-free graph $G$ has a clique or stable set of size at least $|G|^c$; and they proved that this is true with $|G|^c$ replaced by $2^{c\sqrt{\log |G|}}$. \nThere has no improvement on this result (for general $H$) until now\, but now we have an improvement: that for every graph $H$\, there exists $c>0$ such that every $H$-free graph $G$ with $|G|\ge 2$ has a clique or stable set of size at least $$2^{c\sqrt{\log |G|\log\log|G|}}.$$ This talk will outline the proof. \nJoint work with Matija Bucić\, Tung Nguyen and Alex Scott.
URL:https://dimag.ibs.re.kr/event/2023-03-16/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230314T163000
DTEND;TZID=Asia/Seoul:20230314T173000
DTSTAMP:20260416T191942
CREATED:20230120T011459Z
LAST-MODIFIED:20240707T073956Z
UID:6701-1678811400-1678815000@dimag.ibs.re.kr
SUMMARY:Stijn Cambie\, Recent progress on the Union-closed conjecture and related
DESCRIPTION:We give a summary on the work of the last months related to Frankl’s Union-Closed conjecture and its offsprings. The initial conjecture is stated as a theorem in extremal set theory; when a family F is union-closed (the union of sets of F is itself a set of $\mathcal F$)\, then $\mathcal F$ contains an (abundant) element that belongs to at least half of the sets. Meanwhile\, there are many related versions of the conjecture due to Frankl. For example\, graph theorists may prefer the equivalent statement that every bipartite graph has a vertex that belongs to no more than half of the maximal independent sets. While even proving the ε-Union-Closed Sets Conjecture was out of reach\, Poonen and Cui & Hu conjectured already stronger forms. \nAt the end of last year\, progress was made on many of these conjectures. Gilmer proved the ε-Union-Closed Sets Conjecture using an elegant entropy-based method which was sharpened by many others. Despite a sharp approximate form of the union-closed conjecture as stated by Chase and Lovett\, a further improvement was possible. In a different direction\, Kabela\, Polak and Teska constructed union-closed family sets with large sets and few abundant elements. \nThis talk will keep the audience up-to-date and give them insight in the main ideas. \nPeople who would like more details\, can join the Ecopro-reading session on the 14th of March (10 o’clock\, B332) as well. Here we go deeper in the core of the proofs and discuss possible directions for the full resolution.
URL:https://dimag.ibs.re.kr/event/2023-03-14/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230309T100000
DTEND;TZID=Asia/Seoul:20230309T110000
DTSTAMP:20260416T191942
CREATED:20230118T233622Z
LAST-MODIFIED:20240707T074003Z
UID:6685-1678356000-1678359600@dimag.ibs.re.kr
SUMMARY:Marcelo Sales\, On Pisier type problems
DESCRIPTION:A subset $A\subseteq \mathbb Z$ of integers is free if for every two distinct subsets $B\, B’\subseteq A$ we have \[ \sum_{b\in B}b\neq \sum_{b’\in B’} b’.\]Pisier asked if for every subset $A\subseteq \mathbb Z$ of integers the following two statement are equivalent: \n(i) $A$ is a union of finitely many free sets.\n(ii) There exists $\epsilon>0$ such that every finite subset $B\subseteq A$ contains a free subset $C\subseteq B$ with $|C|\geq \epsilon |B|$. \nIn a more general framework\, the Pisier question can be seen as the problem of determining if statements (i) and (ii) are equivalent for subsets of a given structure with prescribed property. We study the problem for several structures including $B_h$-sets\, arithmetic progressions\, independent sets in hypergraphs and configurations in the euclidean space. This is joint work with Jaroslav Nešetřil and Vojtech Rödl.
URL:https://dimag.ibs.re.kr/event/2023-03-09/
LOCATION:Zoom ID: 224 221 2686 (ibsecopro)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230307T163000
DTEND;TZID=Asia/Seoul:20230307T173000
DTSTAMP:20260416T191942
CREATED:20230111T063520Z
LAST-MODIFIED:20240707T074009Z
UID:6655-1678206600-1678210200@dimag.ibs.re.kr
SUMMARY:Eunjin Oh (오은진)\, Parameterized algorithms for the planar disjoint paths problem
DESCRIPTION:Given an undirected planar graph $G$ with $n$ vertices and a set $T$ of $k$ pairs $(s_i\,t_i)_{i=1}^k$ of vertices\, the goal of the planar disjoint paths problem is to find a set $\mathcal P$ of $k$ pairwise vertex-disjoint paths connecting $s_i$ and $t_i$ for all indices $i\in\{1\,\ldots\,k\}$. This problem has been studied extensively due to its numerous applications such as VLSI layout and circuit routing. However\, this problem is NP-complete even for grid graphs. This motivates the study of this problem from the viewpoint of parameterized algorithms. \nIn this talk\, I will present a $2^{O(k^2)}n$-time algorithm for the planar disjoint paths problem. This improves the two previously best-known algorithms: $2^{2^{O(k)}}n$-time algorithm [Discrete Applied Mathematics 1995] and $2^{O(k^2)}n^6$-time algorithm [STOC 2020]. \nThis is joint work with Kyungjin Cho and Seunghyeok Oh.
URL:https://dimag.ibs.re.kr/event/2023-03-07/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230228T163000
DTEND;TZID=Asia/Seoul:20230228T173000
DTSTAMP:20260416T191942
CREATED:20230213T001557Z
LAST-MODIFIED:20240707T074017Z
UID:6782-1677601800-1677605400@dimag.ibs.re.kr
SUMMARY:Maya Sankar\, The Turán Numbers of Homeomorphs
DESCRIPTION:Let $X$ be a 2-dimensional simplicial complex. Denote by $\text{ex}_{\hom}(n\,X)$ the maximum number of 2-simplices in an $n$-vertex simplicial complex that has no sub-simplicial complex homeomorphic to $X$. The asymptotics of $\text{ex}_{\hom}(n\,X)$ have recently been determined for all surfaces $X$. I will discuss these results\, as well as ongoing work bounding $\text{ex}_{\hom}(n\,X)$ for arbitrary 2-dimensional simplicial complexes $X$.
URL:https://dimag.ibs.re.kr/event/2023-02-28/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230222T170000
DTEND;TZID=Asia/Seoul:20230222T180000
DTSTAMP:20260416T191942
CREATED:20221115T011207Z
LAST-MODIFIED:20240707T074027Z
UID:6483-1677085200-1677088800@dimag.ibs.re.kr
SUMMARY:Daniel Altman\, On an arithmetic Sidorenko conjecture\, and a question of Alon
DESCRIPTION:Let $G=\mathbb{F}_p^n$. Which systems of linear equations $\Psi$ have the property that amongst all subsets of $G$ of fixed density\, random subsets minimise the number of solutions to $\Psi$? This is an arithmetic analogue of a well-known conjecture of Sidorenko in graph theory\, which has remained open and of great interest since the 1980s. We will discuss some recent results along these lines\, with particular focus on some of the ideas behind a negative answer to a related question of Alon.
URL:https://dimag.ibs.re.kr/event/2023-02-22/
LOCATION:Zoom ID: 224 221 2686 (ibsecopro)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230221T163000
DTEND;TZID=Asia/Seoul:20230221T173000
DTSTAMP:20260416T191942
CREATED:20230110T061742Z
LAST-MODIFIED:20240705T170041Z
UID:6636-1676997000-1677000600@dimag.ibs.re.kr
SUMMARY:Meike Hatzel\, Fixed-Parameter Tractability of Directed Multicut with Three Terminal Pairs Parametrised by the Size of the Cutset: Twin-Width Meets Flow-Augmentation
DESCRIPTION:We show fixed-parameter tractability of the Directed Multicut problem with three terminal pairs (with a randomized algorithm). This problem\, given a directed graph $G$\, pairs of vertices (called terminals) $(s_1\,t_1)$\, $(s_2\,t_2)$\, and $(s_3\,t_3)$\, and an integer $k$\, asks to find a set of at most $k$ non-terminal vertices in $G$ that intersect all $s_1t_1$-paths\, all $s_2t_2$-paths\, and all $s_3t_3$-paths. The parameterized complexity of this case has been open since Chitnis\, Cygan\, Hajiaghayi\, and Marx proved fixed-parameter tractability of the 2-terminal-pairs case at SODA 2012\, and Pilipczuk and Wahlström proved the W[1]-hardness of the 4-terminal-pairs case at SODA 2016. \nOn the technical side\, we use two recent developments in parameterized algorithms. Using the technique of directed flow-augmentation [Kim\, Kratsch\, Pilipczuk\, Wahlström\, STOC 2022] we cast the problem as a CSP problem with few variables and constraints over a large ordered domain. We observe that this problem can be in turn encoded as an FO model-checking task over a structure consisting of a few 0-1 matrices. We look at this problem through the lenses of twin-width\, a recently introduced structural parameter [Bonnet\, Kim\, Thomassé\, Watrigant\, FOCS 2020]: By a recent characterization [Bonnet\, Giocanti\, Ossona de Mendez\, Simon\, Thomassé\, Toruńczyk\, STOC 2022] the said FO model-checking task can be done in FPT time if the said matrices have bounded grid rank. To complete the proof\, we show an irrelevant vertex rule: If any of the matrices in the said encoding has a large grid minor\, a vertex corresponding to the “middle” box in the grid minor can be proclaimed irrelevant — not contained in the sought solution — and thus reduced.
URL:https://dimag.ibs.re.kr/event/2023-02-21/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
END:VCALENDAR