BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Discrete Mathematics Group - ECPv6.15.20//NONSGML v1.0//EN
CALSCALE:GREGORIAN
METHOD:PUBLISH
X-WR-CALNAME:Discrete Mathematics Group
X-ORIGINAL-URL:https://dimag.ibs.re.kr
X-WR-CALDESC:Events for Discrete Mathematics Group
REFRESH-INTERVAL;VALUE=DURATION:PT1H
X-Robots-Tag:noindex
X-PUBLISHED-TTL:PT1H
BEGIN:VTIMEZONE
TZID:Asia/Seoul
BEGIN:STANDARD
TZOFFSETFROM:+0900
TZOFFSETTO:+0900
TZNAME:KST
DTSTART:20180101T000000
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20200722T163000
DTEND;TZID=Asia/Seoul:20200722T173000
DTSTAMP:20260418T231849
CREATED:20200629T004204Z
LAST-MODIFIED:20240707T083748Z
UID:2563-1595435400-1595439000@dimag.ibs.re.kr
SUMMARY:Paloma T. Lima\, Graph Square Roots of Small Distance from Degree One Graphs
DESCRIPTION:Given a graph class $\mathcal{H}$\, the task of the $\mathcal{H}$-Square Root problem is to decide whether an input graph G has a square root H that belongs to $\mathcal{H}$. We are interested in the parameterized complexity of the problem for classes $\mathcal{H}$ that are composed by the graphs at vertex deletion distance at most $k$ from graphs of maximum degree at most one. That is\, we are looking for a square root H that has a modulator S of size k such that H-S is the disjoint union of isolated vertices and disjoint edges. We show that different variants of the problems with constraints on the number of isolated vertices and edges in H-S are FPT when parameterized by k\, by providing algorithms with running time $2^{2^{O(k)}}\cdot n^{O(1)}$. We further show that the running time of our algorithms is asymptotically optimal and it is unlikely that the double-exponential dependence on k could be avoided. In particular\, we prove that the VC-k Root problem\, that asks whether an input graph has a square root with vertex cover of size at most k\, cannot be solved in time $2^{2^{o(k)}}\cdot n^{O(1)}$ unless the Exponential Time Hypothesis fails. Moreover\, we point out that VC-k Root parameterized by k does not admit a subexponential kernel unless P=NP. \nThis is a joint work with Petr Golovach and Charis Papadopoulos.
URL:https://dimag.ibs.re.kr/event/2020-07-22/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20200721T163000
DTEND;TZID=Asia/Seoul:20200721T173000
DTSTAMP:20260418T231849
CREATED:20200519T123058Z
LAST-MODIFIED:20240707T083754Z
UID:2456-1595349000-1595352600@dimag.ibs.re.kr
SUMMARY:Ilkyoo Choi (최일규)\, Flexibility of Planar Graphs
DESCRIPTION:Oftentimes in chromatic graph theory\, precoloring techniques are utilized in order to obtain the desired coloring result. For example\, Thomassen’s proof for 5-choosability of planar graphs actually shows that two adjacent vertices on the same face can be precolored. In this vein\, we investigate a precoloring extension problem formalized by Dvorak\, Norin\, and Postle named flexibility. Given a list assignment $L$ on a graph $G$\, an $L$-request is a function on a subset $S$ of the vertices that indicates a preferred color in $L(v)$ for each vertex $v\in S$. A graph $G$ is $\varepsilon$-flexible for list size $k$ if given a $k$-list assignment $L$ and an $L$-request\, there is an $L$-coloring of $G$ satisfying an $\varepsilon$-fraction of the requests in $S$. We survey known results regarding this new concept\, and prove some new results regarding flexibility of planar graphs.
URL:https://dimag.ibs.re.kr/event/2020-07-21/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20200714T163000
DTEND;TZID=Asia/Seoul:20200714T173000
DTSTAMP:20260418T231849
CREATED:20200708T123817Z
LAST-MODIFIED:20240707T083801Z
UID:2622-1594744200-1594747800@dimag.ibs.re.kr
SUMMARY:Casey Tompkins\, Inverse Turán Problems
DESCRIPTION:For given graphs $G$ and $F$\, the Turán number $ex(G\,F)$ is defined to be the maximum number of edges in an $F$-free subgraph of $G$. Briggs and Cox introduced a dual version of this problem wherein for a given number $k$\, one maximizes the number of edges in a host graph $G$ for which $ex(G\,H) < k$.  We resolve a problem of Briggs and Cox in the negative by showing that the inverse Turán number of $C_4$ is $\Theta(k^{3/2})$. More generally\, we determine the order of magnitude of the inverse Turán number of $K_{s\,t}$ for all $s$ and $t$.  Addressing another problem of Briggs and Cox\, we determine the asymptotic value of the inverse Turán number of the paths of length $4$ and $5$ and provide an improved lower bound for all paths of even length.  We also obtain improved bounds on the inverse Turán number of even cycles \nJoint work with Ervin Győri\, Nika Salia and Oscar Zamora.
URL:https://dimag.ibs.re.kr/event/2020-07-14/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20200707T163000
DTEND;TZID=Asia/Seoul:20200707T173000
DTSTAMP:20260418T231849
CREATED:20200526T020628Z
LAST-MODIFIED:20240707T083806Z
UID:2481-1594139400-1594143000@dimag.ibs.re.kr
SUMMARY:Seog-Jin Kim (김석진)\, Online DP-coloring of graphs
DESCRIPTION:Online list coloring and DP-coloring are generalizations of list coloring that attracted considerable attention recently. Each of the paint number\, $\chi_P(G)$\, (the minimum number of colors needed for an online coloring of $G$) and the DP-chromatic number\, $\chi_{DP}(G)$\, (the minimum number of colors needed for a DP-coloring of $G$) is at least the list chromatic number\, $\chi_\ell(G)$\, of $G$ and can be much larger. On the other hand\, each of them has a number of useful properties.\nWe introduce a common generalization\, online DP-coloring\, of online list coloring and DP-coloring and to study its properties. This is joint work with Alexandr Kostochka\, Xuer Li\, and Xuding Zhu.
URL:https://dimag.ibs.re.kr/event/2020-07-07/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20200630T163000
DTEND;TZID=Asia/Seoul:20200630T173000
DTSTAMP:20260418T231849
CREATED:20200617T222504Z
LAST-MODIFIED:20240705T200042Z
UID:2542-1593534600-1593538200@dimag.ibs.re.kr
SUMMARY:Dennis Wong\, Generating Gray codes and universal cycles for weak orders
DESCRIPTION:A weak order is a way to rank n objects where ties are allowed. Weak orders have applications in diverse areas such as linguistics\, designing combination locks\, and even in horse racing. In this talk\, we present new and simple algorithms to generate Gray codes and universal cycles for weak orders.
URL:https://dimag.ibs.re.kr/event/2020-06-30/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20200623T163000
DTEND;TZID=Asia/Seoul:20200623T173000
DTSTAMP:20260418T231849
CREATED:20200611T051100Z
LAST-MODIFIED:20240707T083929Z
UID:2529-1592929800-1592933400@dimag.ibs.re.kr
SUMMARY:Jaehoon Kim (김재훈)\, A resilience version of Pósa's theorem
DESCRIPTION:Pósa’s theorem states that any graph G whose degree sequence $d_1\leq \dots \leq d_n$ satisfies $d_i \geq i+1$ for all $i< n/2$ has a Hamilton cycle. This degree condition is best possible. We show that a similar result holds for suitable subgraphs $G$ of random graphs. This is joint work with Padraig Condon\, Alberto Espuny Diaz\, Daniela Kühn and Deryk Osthus.
URL:https://dimag.ibs.re.kr/event/2020-06-23/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20200616T163000
DTEND;TZID=Asia/Seoul:20200616T173000
DTSTAMP:20260418T231849
CREATED:20200525T080845Z
LAST-MODIFIED:20240707T083941Z
UID:2478-1592325000-1592328600@dimag.ibs.re.kr
SUMMARY:Andreas Holmsen\, Fractional Helly and topological complexity
DESCRIPTION:The fractional Helly theorem is a simple yet remarkable generalization of Helly’s classical theorem on the intersection of convex sets\, and it is of considerable interest to extend the fractional Helly theorem beyond the setting of convexity. In this talk I will discuss a recent result which shows that the fractional Helly theorem holds for families of subsets of $\mathbb R^d$ which satisfy only very weak topological assumptions. The proofs combine a number of tools such as homological minors\, stair-convexity\, supersaturation in hypergraphs\, Radon dimension\, and Ramsey-type arguments. This is joint work with Xavier Goaoc and Zuzana Patáková.
URL:https://dimag.ibs.re.kr/event/2020-06-16/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20200609T163000
DTEND;TZID=Asia/Seoul:20200609T173000
DTSTAMP:20260418T231849
CREATED:20200529T052601Z
LAST-MODIFIED:20240705T200042Z
UID:2498-1591720200-1591723800@dimag.ibs.re.kr
SUMMARY:Jiseung Kim (김지승)\, Hardness and concrete security in cryptography
DESCRIPTION:Computationally hard problems have been widely used to construct cryptographic primitives such as encryptions\, digital signatures. For example\, provably secure primitives are based on a reduction from the hardness problems. However\, the concrete instantiation of primitives does not follow the results of hardness problems due to its efficiency. In this talk\, we introduce cryptographic hardness problems widely used in cryptography and the gap between hardness results and concrete security of cryptographic primitives based on our recent works.
URL:https://dimag.ibs.re.kr/event/2020-06-09/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20200602T163000
DTEND;TZID=Asia/Seoul:20200602T173000
DTSTAMP:20260418T231849
CREATED:20200528T061536Z
LAST-MODIFIED:20240705T200043Z
UID:2491-1591115400-1591119000@dimag.ibs.re.kr
SUMMARY:Huy-Tung Nguyen\, The average cut-rank of graphs
DESCRIPTION:The cut-rank of a set X of vertices in a graph G is defined as the rank of the X×(V(G)∖X) matrix over the binary field whose (i\,j)-entry is 1 if the vertex i in X is adjacent to the vertex j in V(G)∖X and 0 otherwise. We introduce the graph parameter called the average cut-rank of a graph\, defined as the expected value of the cut-rank of a random set of vertices. We show that this parameter does not increase when taking vertex-minors of graphs and a class of graphs has bounded average cut-rank if and only if it has bounded neighborhood diversity. This allows us to deduce that for each real α\, the list of induced-subgraph-minimal graphs having average cut-rank larger than (or at least) α is finite. We further refine this by providing an upper bound on the size of obstruction and a lower bound on the number of obstructions for average cut-rank at most (or smaller than) α for each real α≥0. Finally\, we describe explicitly all graphs of average cut-rank at most 3/2 and determine up to 3/2 all possible values that can be realized as the average cut-rank of some graph. This is joint work with Sang-il Oum.
URL:https://dimag.ibs.re.kr/event/2020-06-02/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20200526T163000
DTEND;TZID=Asia/Seoul:20200526T173000
DTSTAMP:20260418T231849
CREATED:20200507T062724Z
LAST-MODIFIED:20240705T201016Z
UID:2430-1590510600-1590514200@dimag.ibs.re.kr
SUMMARY:Hong Liu (刘鸿)\, Asymptotic Structure for the Clique Density Theorem
DESCRIPTION:The famous Erdős-Rademacher problem asks for the smallest number of r-cliques in a graph with the given number of vertices and edges. Despite decades of active attempts\, the asymptotic value of this extremal function for all r was determined only recently\, by Reiher [Annals of Mathematics\, 184 (2016) 683-707]. Here we describe the asymptotic structure of all almost extremal graphs. This task for r=3 was previously accomplished by Pikhurko and Razborov [Combinatorics\, Probability and Computing\, 26 (2017) 138–160].
URL:https://dimag.ibs.re.kr/event/2020-05-26/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20200519T163000
DTEND;TZID=Asia/Seoul:20200519T173000
DTSTAMP:20260418T231849
CREATED:20200422T003736Z
LAST-MODIFIED:20240705T201022Z
UID:2383-1589905800-1589909400@dimag.ibs.re.kr
SUMMARY:O-joung Kwon (권오정)\,  Mim-width: a width parameter beyond rank-width
DESCRIPTION:Vatshelle (2012) introduced a width parameter called mim-width. It is based on the following cut function : for a vertex partition (A\,B) of a graph\, the complexity of this partition is computed by the size of a maximum induced matching of the bipartite subgraph induced by edges between A and B. This parameter naturally extends the expressibility power of the graph parameters clique-width and rank-width\, which have been well-developed in recent years. In a series of papers\, we explored the computational complexity of several problems\, parameterized by mim-width. We summarize known structural properties and algorithmic applications of mim-width\, and give some open problems at the end. This is joint work with Lars Jaffke\, Torstein Strømme\, and Jan Arne Telle.
URL:https://dimag.ibs.re.kr/event/2020-05-19/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20200512T163000
DTEND;TZID=Asia/Seoul:20200512T173000
DTSTAMP:20260418T231849
CREATED:20200417T054420Z
LAST-MODIFIED:20240707T084008Z
UID:2354-1589301000-1589304600@dimag.ibs.re.kr
SUMMARY:Eun Jung Kim (김은정)\, Twin-width: tractable FO model checking
DESCRIPTION:Inspired by a width invariant defined on permutations by Guillemot and Marx [SODA ’14]\, we introduce the notion of twin-width on graphs and on matrices. Proper minor-closed classes\, bounded rank-width graphs\, map graphs\, $K_t$-free unit $d$-dimensional ball graphs\, posets with antichains of bounded size\, and proper subclasses of dimension-2 posets all have bounded twin-width. On all these classes (except map graphs without geometric embedding) we show how to compute in polynomial time a sequence of $d$-contractions\, witness that the twin-width is at most $d$. We show that FO model checking\, that is deciding if a given first-order formula $\phi$ evaluates to true for a given binary structure $G$ on a domain $D$\, is FPT in $|\phi|$ on classes of bounded twin-width\, provided the witness is given. More precisely\, being given a $d$-contraction sequence for $G$\, our algorithm runs in time $f(d\,|\phi|) \cdot |D|$ where $f$ is a computable but non-elementary function. We also prove that bounded twin-width is preserved by FO interpretations and transductions (allowing operations such as squaring or complementing a graph). This unifies and significantly extends the knowledge on fixed-parameter tractability of FO model checking on non-monotone classes\, such as the FPT algorithm on bounded-width posets by Gajarský et al. [FOCS ’15]. \nIn order to explore the limits of twin-width\, we generalize to bounded twin-width classes a result by Norine et al. [JCTB ’06] stating that proper minor-free classes are small (i.e.\, they contain at most $n! c^n$ graphs on $n$ vertices\, for some constant $c$). This implies by a counting argument that bounded-degree graphs\, interval graphs\, and unit disk graphs have unbounded twin-width. \nJoint work with Stéphan Thomassé\, Édouard Bonnet\, and Rémi Watrigant.
URL:https://dimag.ibs.re.kr/event/2020-05-12/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;VALUE=DATE:20200508
DTEND;VALUE=DATE:20200510
DTSTAMP:20260418T231849
CREATED:20200221T012551Z
LAST-MODIFIED:20240705T201209Z
UID:2142-1588896000-1589068799@dimag.ibs.re.kr
SUMMARY:KSIAM 2020 Spring Conference (cancelled)
DESCRIPTION:KSIAM 2020 Spring Conference will be held at IBS from May 8\, 2020 to May 9\, 2020. \nOrganized by Korean Society for Industrial and Applied Mathematics. \nOrganizing Committee\n\nMyungjoo Kang (Seoul National University) (chair)\nAhn\, Jaemyung (KAIST)\nKwon\, Hee-Dae (Inha University)\nLee\, Eun Jung (Yonsei University)\nJang\, Bongsoo (UNIST)\nJung\, Miyoun (Hankuk University of Foreign Studies)\nKim\, Junseok (Korea University)\nOum\, Sang-il (IBS\, KAIST)
URL:https://dimag.ibs.re.kr/event/ksiam-2020-spring-conference/
LOCATION:IBS Science Culture Center
CATEGORIES:Workshops and Conferences
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20200428T163000
DTEND;TZID=Asia/Seoul:20200428T173000
DTSTAMP:20260418T231849
CREATED:20200417T080351Z
LAST-MODIFIED:20240707T084026Z
UID:2361-1588091400-1588095000@dimag.ibs.re.kr
SUMMARY:Seunghun Lee (이승훈)\, Leray numbers of complexes of graphs with bounded matching number
DESCRIPTION:Given a graph $G$ on the vertex set $V$\, the non-matching complex of $G$\, $\mathsf{NM}_k(G)$\, is the family of subgraphs $G’ \subset G$ whose matching number $\nu(G’)$ is strictly less than $k$. As an attempt to generalize the result by Linusson\, Shareshian and Welker on the homotopy types of $\mathsf{NM}_k(K_n)$ and $\mathsf{NM}_k(K_{r\,s})$ to arbitrary graphs $G$\, we show that (i) $\mathsf{NM}_k(G)$ is $(3k-3)$-Leray\, and (ii) if $G$ is bipartite\, then $\mathsf{NM}_k(G)$ is $(2k-2)$-Leray. This result is obtained by analyzing the homology of the links of non-empty faces of the complex $\mathsf{NM}_k(G)$\, which vanishes in all dimensions $d\geq 3k-4$\, and all dimensions $d \geq 2k-3$ when $G$ is bipartite. As a corollary\, we have the following rainbow matching theorem which generalizes the result by Aharoni et. al. and Drisko’s theorem: Let $E_1\, \dots\, E_{3k-2}$ be non-empty edge subsets of a graph and suppose that $\nu(E_i\cup E_j)\geq k$ for every $i\ne j$. Then $E=\bigcup E_i$ has a rainbow matching of size $k$. Furthermore\, the number of edge sets $E_i$ can be reduced to $2k-1$ when $E$ is the edge set of a bipartite graph. \nThis is a joint work with Andreas Holmsen.
URL:https://dimag.ibs.re.kr/event/2020-04-28/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20200421T163000
DTEND;TZID=Asia/Seoul:20200421T173000
DTSTAMP:20260418T231849
CREATED:20200417T000545Z
LAST-MODIFIED:20240705T201135Z
UID:2349-1587486600-1587490200@dimag.ibs.re.kr
SUMMARY:Sang-il Oum (엄상일)\, Survey on vertex-minors
DESCRIPTION:For a vertex v of a graph G\, the local complementation at v is an operation to obtain a new graph denoted by G*v from G such that two distinct vertices x\, y are adjacent in G*v if and only if both x\, y are neighbors of v and x\, y are non-adjacent\, or at least one of x\, y is not a neighbor of v and x\, y are adjacent. A graph H is a vertex-minor of a graph G if H is obtained from G by a sequence of local complementation and vertex deletions. Interestingly vertex-minors have been used in the study of measurement-based quantum computing on graph states. \nMotivated by the big success of the graph minor structure theory developed deeply by Robertson and Seymour since 1980s\, we propose a similar theory for vertex-minors. This talk will illustrate similarities between graph minors and graph vertex-minors and give a survey of known theorems and open problems on vertex-minors of graphs.
URL:https://dimag.ibs.re.kr/event/2020-04-21/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20200414T163000
DTEND;TZID=Asia/Seoul:20200414T173000
DTSTAMP:20260418T231849
CREATED:20200409T030201Z
LAST-MODIFIED:20240705T201139Z
UID:2322-1586881800-1586885400@dimag.ibs.re.kr
SUMMARY:Casey Tompkins\, Saturation problems in the Ramsey theory of graphs\, posets and point sets
DESCRIPTION:In 1964\, Erdős\, Hajnal and Moon introduced a saturation version of Turán’s classical theorem in extremal graph theory. In particular\, they determined the minimum number of edges in a $K_r$-free\, $n$-vertex graph with the property that the addition of any further edge yields a copy of $K_r$. We consider analogues of this problem in other settings. We prove a saturation version of the Erdős-Szekeres theorem about monotone subsequences and saturation versions of some Ramsey-type theorems on graphs and Dilworth-type theorems on posets. \nWe also consider semisaturation problems\, wherein we allow the family to have the forbidden configuration\, but insist that any addition to the family yields a new copy of the forbidden configuration. In this setting\, we prove a semisaturation version of the Erdős-Szekeres theorem on convex $k$-gons\, as well as multiple semisaturation theorems for sequences and posets. \nThis project was joint work with Gábor Damásdi\, Balázs Keszegh\, David Malec\, Zhiyu Wang and Oscar Zamora.
URL:https://dimag.ibs.re.kr/event/2020-04-14/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20200407T163000
DTEND;TZID=Asia/Seoul:20200407T173000
DTSTAMP:20260418T231849
CREATED:20200403T043936Z
LAST-MODIFIED:20240707T084138Z
UID:2269-1586277000-1586280600@dimag.ibs.re.kr
SUMMARY:Pascal Gollin\, Disjoint dijoins for classes of dibonds in finite and infinite digraphs
DESCRIPTION:A dibond in a directed graph is a bond (i.e. a minimal non-empty cut) for which all of its edges are directed to a common side of the cut. A famous theorem of Lucchesi and Younger states that in every finite digraph the least size of an edge set meeting every dicut equals the maximum number of disjoint dibonds in that digraph. We call such sets dijoins. \nWoodall conjectured a dual statement. He asked whether the maximum number of disjoint dijoins in a digraph equals the minimum size of a dibond.\nWe study a modification of this question where we restrict our attention to certain classes of dibonds\, i.e. whether for a class $\mathfrak{B}$ of dibonds of a digraph the maximum number of disjoint edge sets meeting every dibond in $\mathfrak{B}$ equal the size a minimum dibond in $\mathfrak{B}$. \nIn particular\, we verify this questions for nested classes of dibonds\, for the class of dibonds of minimum size\, and for classes of infinite dibonds.
URL:https://dimag.ibs.re.kr/event/2020-04-07/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20200331T163000
DTEND;TZID=Asia/Seoul:20200331T173000
DTSTAMP:20260418T231849
CREATED:20200324T132402Z
LAST-MODIFIED:20240707T084146Z
UID:2222-1585672200-1585675800@dimag.ibs.re.kr
SUMMARY:Ringi Kim (김린기)\, The strong clique number of graphs with forbidden cycles
DESCRIPTION:The strong clique number of a graph $G$ is the maximum size of a set of edges of which every pair has distance at most two. \nIn this talk\, we prove that every  $\{C_5\,C_{2k}\}$-free graph has strong clique number at most $k\Delta(G)-(k-1)$\, which resolves a conjecture by  Cames van Batenburg et al. We also prove that every $C_{2k}$-free graph has strong clique number at most $(2k−1)\Delta(G) + (2k−1)^2$\, improving the previous known upper bound $10k^2 (\Delta(G)-1)$ due to  Cames van Batenburg et al. This is joint work with Eun-Kyung Cho\, Ilkyoo Choi\, and Boram Park.
URL:https://dimag.ibs.re.kr/event/2020-03-31/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20200324T163000
DTEND;TZID=Asia/Seoul:20200324T173000
DTSTAMP:20260418T231849
CREATED:20200311T074415Z
LAST-MODIFIED:20240707T084154Z
UID:2186-1585067400-1585071000@dimag.ibs.re.kr
SUMMARY:Kevin Hendrey\, Covering radius in the Hamming permutation space
DESCRIPTION:Our problem can be described in terms of a two player game\, played with the set $\mathcal{S}_n$ of permutations on $\{1\,2\,\dots\,n\}$. First\, Player 1 selects a subset $S$ of $\mathcal{S}_n$ and shows it to Player 2. Next\, Player 2 selects a permutation $p$ from $\mathcal{S}_n$ as different as possible from the permutations in $S$\, and shows it to Player 1. Finally\, Player 1 selects a permutation $q$ from $S$\, and they compare $p$ and $q$. The aim of Player 1 is to ensure that $p$ and $q$ differ in few positions\, while keeping the size of $S$ small. The function $f(n\,s)$ can be defined as the minimum size of a set $S\subseteq \mathcal{S}_n$ that Player 1 can select in order to gaurantee that $p$ and $q$ will differ in at most $s$ positions. \nI will present some recent results on the function $f(n\,s)$. We are particularly interested in determining the value $f(n\,2)$\, which would resolve a conjecture of Kézdy and Snevily that implies several famous conjectures for Latin squares. Here we improve the best known lower bound\, showing that $f(n\,2)\geqslant 3n/4$. This talk is based on joint work with Ian M. Wanless.
URL:https://dimag.ibs.re.kr/event/2020-03-24/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20200317T163000
DTEND;TZID=Asia/Seoul:20200317T173000
DTSTAMP:20260418T231849
CREATED:20200307T133007Z
LAST-MODIFIED:20240705T201209Z
UID:2180-1584462600-1584466200@dimag.ibs.re.kr
SUMMARY:Dabeen Lee (이다빈)\, On a generalization of the Chvátal-Gomory closure
DESCRIPTION:Integer programming is the problem of optimizing a linear function over the set of integer solutions satisfying a system of inequalities. The most successful technique in practice is the so-called “cutting-plane” algorithm in combination with branch-and-bound enumeration. Cutting-planes for an integer linear program are linear inequalities that are valid for all integer feasible solutions but cut off intermediate fractional solutions. \nThe Chvátal-Gomory cuts\, introduced by Gomory in 1958 and further studied by Chvátal in 1973 in relation to their applications in combinatorial optimization\, are the first class of general-purpose cutting-planes in the literature. The split cuts\, whose name was coined by Cook\, Kannan\, and Schrijver in 1980\, are another class of important cutting-planes in modern integer programming. Although there are infinitely many cuts in each class\, it is known that only finitely many of them are nonredundant\, which is related to designing a finite-convergent cutting-plane algorithm. In this talk\, we introduce a new class of cutting-planes that generalizes the Chvátal-Gomory cuts and generalizes a special case of the split cuts. As the two classic classes of cutting-planes\, we show that only a finite number of cuts can be redundant. \nThis talk is based on a joint work with Sanjeeb Dash and Oktay Günlük.
URL:https://dimag.ibs.re.kr/event/2020-03-17/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20200303T163000
DTEND;TZID=Asia/Seoul:20200303T173000
DTSTAMP:20260418T231849
CREATED:20200207T093644Z
LAST-MODIFIED:20240707T091837Z
UID:2099-1583253000-1583256600@dimag.ibs.re.kr
SUMMARY:Eun-Kyung Cho (조은경)\, Decomposition of a planar graph into a $d$-degenerate graph and a graph with maximum degree at most $h$
DESCRIPTION:Given a graph $G$\, a decomposition of $G$ is a collection of spanning subgraphs $H_1\, \ldots\, H_t$ of $G$ such that each edge of $G$ is an edge of $H_i$ for exactly one $i \in \{1\, \ldots\, t\}$. Given a positive integer $d$\, a graph is said to be $d$-degenerate if every subgraph of it has a vertex of degree at most $d$. Given a non-negative integer $h$\, we say that a graph $G$ is $(d\,h)$-decomposable if there is a decomposition of $G$ into two spanning subgraphs\, where one is a $d$-degenerate graph\, and the other is a graph with maximum degree at most $h$. \nIt is known that a planar graph is $5$-degenerate\, but not always $4$-degenerate. This implies that a planar graph is $(5\,0)$-decomposable\, but not always $(4\,0)$-decomposable. Moreover\, by related previous results\, it is known that a planar graph is $(3\,4)$- and $(2\,8)$-decomposable. \nIn this talk\, we improve these results by showing that every planar graph is $(4\,1)$-\, $(3\,2)$-\, and $(2\,6)$-decomposable. The $(4\,1)$- and $(3\,2)$-decomposabilities are sharp in the sense that the maximum degree condition cannot be reduced more. \nThis is joint work with Ilkyoo Choi\, Ringi Kim\, Boram Park\, Tingting Shan\, and Xuding Zhu.
URL:https://dimag.ibs.re.kr/event/2020-03-03/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20200225T163000
DTEND;TZID=Asia/Seoul:20200225T173000
DTSTAMP:20260418T231849
CREATED:20200217T133320Z
LAST-MODIFIED:20240707T084212Z
UID:2129-1582648200-1582651800@dimag.ibs.re.kr
SUMMARY:Xin Zhang (张欣)\, On the equitable tree-coloring of graphs with low degeneracy
DESCRIPTION:A (vertex) $k$-coloring of a graph $G$ is a tree-coloring if each color class induces a forest\, and is equitable if the sizes of any two color classes differ by at most 1. The first relative result concerning the equitable tree-coloring of graphs is due to H. Fan\, H. A. Kierstead\, G. Liu\, T. Molla\, J.-L. Wu\, and X. Zhang (2011)\, who proved that any graph with maximum degree at most $\Delta$ has a $\Delta$-coloring so that each color class induces a graph with maximum degree at most 1. After that\, many results on this topic were published in the literature. For example\, L. Esperet\, L. Lemoine\, and F. Maffray (2015) showed that any planar graph admits an equitable tree-$k$-coloring for every integer $k\ge 4$，and G. Chen\, Y. Gao\, S. Shan\, G. Wang\, and J.-L. Wu (2017) proved that any 5-degenerate graph with maximum degree at most $\Delta$ admits an equitable tree-$k$-coloring for every $k\geq \lceil\frac{\Delta+1}{2}\rceil$. \nIn this talk\, we review part of the known results and the conjectures on the equitable tree-coloring of graphs\, and then show the sketch proofs of our three new results as follows: \n(a) the vertex set of any graph $G$ can be equitably partitioned into $k$ subsets for any integer $k\geq\max\{\lceil\frac{\Delta(G)+1}{2}\rceil\,\lceil\frac{|G|}{4}\rceil\}$ so that each of them induces a linear forest; \n(b) any plane graph with independent crossings admits an equitable tree-$k$-coloring for every integer $k\ge 8$; \n(c) any $d$-degenerate graph with maximum degree at most $\Delta$ admits an equitable tree-$k$-coloring for every integer $k\geq (\Delta+1)/2$ provided that $\Delta\geq 10d$. \nThis is a joint work with Yuping Gao\, Bi Li\, Yan Li\, and Bei Niu.
URL:https://dimag.ibs.re.kr/event/2020-02-25/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20200218T163000
DTEND;TZID=Asia/Seoul:20200218T173000
DTSTAMP:20260418T231849
CREATED:20200114T112946Z
LAST-MODIFIED:20240705T202042Z
UID:2039-1582043400-1582047000@dimag.ibs.re.kr
SUMMARY:Dong Yeap Kang (강동엽)\, Fragile minor-monotone parameters under random edge perturbation
DESCRIPTION:We investigate how minor-monotone graph parameters change if we add a few random edges to a connected graph $H$. Surprisingly\, after adding a few random edges\, its treewidth\, treedepth\, genus\, and the size of a largest complete minor become very large regardless of the shape of $H$. Our results are close to best possible for various cases. We also discuss analogous results for randomly perturbed bipartite graphs as well as the size of a largest complete odd minor in randomly perturbed graphs.
URL:https://dimag.ibs.re.kr/event/2020-02-18/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20200128T163000
DTEND;TZID=Asia/Seoul:20200128T173000
DTSTAMP:20260418T231849
CREATED:20191216T045747Z
LAST-MODIFIED:20240705T203007Z
UID:1940-1580229000-1580232600@dimag.ibs.re.kr
SUMMARY:Dillon Mayhew\, Courcelle's Theorem for hypergraphs
DESCRIPTION:Courcelle’s Theorem is an influential meta-theorem published in 1990. It tells us that a property of graph can be tested in polynomial time\, as long as the property can expressed in the monadic second-order logic of graphs\, and as long as the input is restricted to a class of graphs with bounded tree-width. There are several properties that are NP-complete in general\, but which can be expressed in monadic logic (3-colourability\, Hamiltonicity…)\, so Courcelle’s Theorem implies that these difficult properties can be tested in polynomial time when the structural complexity of the input is limited. \nMatroids can be considered as a special class of hypergraphs. Any finite set of vectors over a field leads to a matroid\, and such a matroid is said to be representable over that field. Hlineny produced a matroid analogue of Courcelle’s Theorem for input classes with bounded branch-width that are representable over a finite field. \nWe have now identified the structural properties of hypergraph classes that allow a proof of Hliněný’s Theorem to go through. This means that we are able to extend his theorem to several other natural classes of matroids. \nThis talk will contain an introduction to matroids\, monadic logic\, and tree-automata. \nThis is joint work with Daryl Funk\, Mike Newman\, and Geoff Whittle.
URL:https://dimag.ibs.re.kr/event/2020-01-28/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20200120T163000
DTEND;TZID=Asia/Seoul:20200120T173000
DTSTAMP:20260418T231849
CREATED:20200108T022511Z
LAST-MODIFIED:20240705T202052Z
UID:1997-1579537800-1579541400@dimag.ibs.re.kr
SUMMARY:Adam Zsolt Wagner\, The largest projective cube-free subsets of $Z_{2^n}$
DESCRIPTION:What is the largest subset of $Z_{2^n}$ that doesn’t contain a projective d-cube? In the Boolean lattice\, Sperner’s\, Erdos’s\, Kleitman’s and Samotij’s theorems state that families that do not contain many chains must have a very specific layered structure. We show that if instead of $Z_2^n$ we work in $Z_{2^n}$\, analogous statements hold if one replaces the word k-chain by projective cube of dimension $2^{k-1}$. The largest d-cube-free subset of $Z_{2^n}$\, if d is not a power of two\, exhibits a much more interesting behaviour. \nThis is joint work with Jason Long.
URL:https://dimag.ibs.re.kr/event/2020-01-20/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20200115T163000
DTEND;TZID=Asia/Seoul:20200115T173000
DTSTAMP:20260418T231849
CREATED:20200107T040041Z
LAST-MODIFIED:20240707T084237Z
UID:1990-1579105800-1579109400@dimag.ibs.re.kr
SUMMARY:Ben Lund\, Furstenberg sets over finite fields
DESCRIPTION:An important family of incidence problems are discrete analogs of deep questions in geometric measure theory. Perhaps the most famous example of this is the finite field Kakeya conjecture\, proved by Dvir in 2008. Dvir’s proof introduced the polynomial method to incidence geometry\, which led to the solution to many long-standing problems in the area.\nI will talk about a generalization of the Kakeya conjecture posed by Ellenberg\, Oberlin\, and Tao. A $(k\,m)$-Furstenberg set S in $\mathbb F_q^n$ has the property that\, parallel to every affine $k$-plane V\, there is a k-plane W such that $|W \cap S| > m$. Using sophisticated ideas from algebraic geometry\, Ellenberg and Erman showed that if S is a $(k\,m)$-Furstenberg set\, then $|S| > c m^{n/k}$\, for a constant c depending on n and k. In recent joint work with Manik Dhar and Zeev Dvir\, we give simpler proofs of stronger bounds. For example\, if $m>2^{n+7}q$\, then $|S|=(1-o(1))mq^{n-k}$\, which is tight up to the $o(1)$ term.
URL:https://dimag.ibs.re.kr/event/2020-01-15/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20200114T163000
DTEND;TZID=Asia/Seoul:20200114T173000
DTSTAMP:20260418T231849
CREATED:20191225T230320Z
LAST-MODIFIED:20240705T202054Z
UID:1961-1579019400-1579023000@dimag.ibs.re.kr
SUMMARY:Sanjeeb Dash\, Boolean decision rules via column generation
DESCRIPTION:In many applications of machine learning\, interpretable or explainable models for binary classification\, such as decision trees or decision lists\, are preferred over potentially more accurate but less interpretable models such as random forests or support vector machines. In this talk\, we consider boolean decision rule sets (equivalent to boolean functions in disjunctive normal form) as interpretable models for binary classification. We define the complexity of a rule set to be the number of rules (clauses) plus the number of conditions (literals) across all clauses\, and assume that simpler or less complex models are more interpretable. We discuss an integer programming formulation for such models that trades off classification accuracy against rule simplicity\, and obtain high-quality classifiers of this type using column generation techniques. Compared to some recent alternatives\, our algorithm dominates the accuracy-simplicity trade-off in 8 out of 16 datasets\, and also produced the winning entry in the 2018 FICO explainable machine learning challenge. When compared to rule learning methods designed for accuracy\, our algorithm sometimes finds significantly simpler solutions that are no less accurate.
URL:https://dimag.ibs.re.kr/event/2020-01-14/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20191226T163000
DTEND;TZID=Asia/Seoul:20191226T173000
DTSTAMP:20260418T231849
CREATED:20191122T072031Z
LAST-MODIFIED:20240705T203023Z
UID:1875-1577377800-1577381400@dimag.ibs.re.kr
SUMMARY:Jaiung Jun (전재웅)\, The Hall algebra of the category of matroids
DESCRIPTION:To an abelian category A satisfying certain finiteness conditions\, one can associate an algebra H_A (the Hall algebra of A) which encodes the structures of the space of extensions between objects in A. For a non-additive setting\, Dyckerhoff and Kapranov introduced the notion of proto-exact categories\, as a non-additive generalization of an exact category\, which is shown to suffice for the construction of an associative Hall algebra. In this talk\, I will discuss the category of matroids in this perspective.
URL:https://dimag.ibs.re.kr/event/2019-12-26/
LOCATION:Room 1401\, Bldg. E6-1\, KAIST
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20191219T163000
DTEND;TZID=Asia/Seoul:20191219T173000
DTSTAMP:20260418T231849
CREATED:20191119T013103Z
LAST-MODIFIED:20240707T084251Z
UID:1801-1576773000-1576776600@dimag.ibs.re.kr
SUMMARY:Attila Joó\, Base partition for finitary-cofinitary matroid families
DESCRIPTION:Let ${\mathcal{M} = (M_i \colon i\in K)}$ be a finite or infinite family consisting of finitary and cofinitary matroids on a common ground set $E$. \nWe prove the following Cantor-Bernstein-type result: if $E$ can be covered by sets ${(B_i \colon i\in K)}$ which are bases in the corresponding matroids and there are also pairwise disjoint bases of the matroids $M_i$ then $E$ can be partitioned into bases with respect to $\mathcal{M}$.
URL:https://dimag.ibs.re.kr/event/2019-12-19/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20191212T163000
DTEND;TZID=Asia/Seoul:20191212T173000
DTSTAMP:20260418T231849
CREATED:20191122T071803Z
LAST-MODIFIED:20240707T084259Z
UID:1872-1576168200-1576171800@dimag.ibs.re.kr
SUMMARY:Hong Liu\, A proof of Mader's conjecture on large clique subdivisions in $C_4$-free graphs
DESCRIPTION:Given any integers $s\,t\geq 2$\, we show there exists some $c=c(s\,t)>0$ such that any $K_{s\,t}$-free graph with average degree $d$ contains a subdivision of a clique with at least $cd^{\frac{1}{2}\frac{s}{s-1}}$ vertices. In particular\, when $s=2$ this resolves in a strong sense the conjecture of Mader in 1999 that every $C_4$-free graph has a subdivision of a clique with order linear in the average degree of the original graph. In general\, the widely conjectured asymptotic behaviour of the extremal density of $K_{s\,t}$-free graphs suggests our result is tight up to the constant $c(s\,t)$. This is joint work with Richard Montgomery.
URL:https://dimag.ibs.re.kr/event/2019-12-12/
LOCATION:Room 1401\, Bldg. E6-1\, KAIST
CATEGORIES:Discrete Math Seminar
END:VEVENT
END:VCALENDAR