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PRODID:-//Discrete Mathematics Group - ECPv6.15.20//NONSGML v1.0//EN
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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:20190101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20200512T163000
DTEND;TZID=Asia/Seoul:20200512T173000
DTSTAMP:20260420T045308
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
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20200519T163000
DTEND;TZID=Asia/Seoul:20200519T173000
DTSTAMP:20260420T045308
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:20200526T163000
DTEND;TZID=Asia/Seoul:20200526T173000
DTSTAMP:20260420T045308
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
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