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PRODID:-//Discrete Mathematics Group - ECPv5.16.4//NONSGML v1.0//EN
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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
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DTSTART:20210101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211102T163000
DTEND;TZID=Asia/Seoul:20211102T173000
DTSTAMP:20220811T141948
CREATED:20211109T073000Z
LAST-MODIFIED:20211027T072258Z
UID:4780-1635870600-1635874200@dimag.ibs.re.kr
SUMMARY:Ben Lund\, Maximal 3-wise intersecting families
DESCRIPTION:A family $\mathcal F$ of subsets of {1\,2\,…\,n} is called maximal k-wise intersecting if every collection of at most k members from $\mathcal F$ has a common element\, and moreover\, no set can be added to $\mathcal F$ while preserving this property. In 1974\, Erdős and Kleitman asked for the smallest possible size of a maximal k-wise intersecting family\, for k≥3. We resolve this problem for k=3 and n even and sufficiently large. \nThis is joint work with Kevin Hendrey\, Casey Tompkins\, and Tuan Tran.
URL:https://dimag.ibs.re.kr/event/2021-11-02/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211109T163000
DTEND;TZID=Asia/Seoul:20211109T173000
DTSTAMP:20220811T141948
CREATED:20211109T073000Z
LAST-MODIFIED:20211027T072336Z
UID:4588-1636475400-1636479000@dimag.ibs.re.kr
SUMMARY:Jaehoon Kim (김재훈)\, 2-complexes with unique embeddings in 3-space
DESCRIPTION:A well-known theorem of Whitney states that a 3-connected planar graph admits an essentially unique embedding into the 2-sphere. We prove a 3-dimensional analogue: a simply-connected 2-complex every link graph of which is 3-connected admits an essentially unique locally flat embedding into the 3-sphere\, if it admits one at all. This can be thought of as a generalisation of the 3-dimensional Schoenflies theorem. This is joint work with Agelos Georgakopoulos.
URL:https://dimag.ibs.re.kr/event/2021-11-09/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211123T163000
DTEND;TZID=Asia/Seoul:20211123T173000
DTSTAMP:20220811T141948
CREATED:20211123T073000Z
LAST-MODIFIED:20211115T023536Z
UID:4798-1637685000-1637688600@dimag.ibs.re.kr
SUMMARY:Casey Tompkins\, Ramsey numbers of Boolean lattices
DESCRIPTION:The poset Ramsey number $R(Q_{m}\,Q_{n})$ is the smallest integer $N$ such that any blue-red coloring of the elements of the Boolean lattice $Q_{N}$ has a blue induced copy of $Q_{m}$ or a red induced copy of $Q_{n}$. Axenovich and Walzer showed that $n+2\le R(Q_{2}\,Q_{n})\le2n+2$. Recently\, Lu and Thompson\nimproved the upper bound to $\frac{5}{3}n+2$. In this paper\, we solve this problem asymptotically by showing that $R(Q_{2}\,Q_{n})=n+O(n/\log n)$.\nJoint work with Dániel Grósz and Abhishek Methuku.
URL:https://dimag.ibs.re.kr/event/2021-11-23/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211130T163000
DTEND;TZID=Asia/Seoul:20211130T173000
DTSTAMP:20220811T141948
CREATED:20211130T073000Z
LAST-MODIFIED:20211204T005349Z
UID:4852-1638289800-1638293400@dimag.ibs.re.kr
SUMMARY:Seonghyuk Im (임성혁)\, Large clique subdivisions in graphs without small dense subgraphs
DESCRIPTION:What is the largest number $f(d)$ where every graph with average degree at least $d$ contains a subdivision of $K_{f(d)}$? Mader asked this question in 1967 and $f(d) = \Theta(\sqrt{d})$ was proved by Bollobás and Thomason and independently by Komlós and Szemerédi. This is best possible by considering a disjoint union of $K_{d\,d}$. However\, this example contains a much smaller subgraph with the almost same average degree\, for example\, one copy of $K_{d\,d}$. \nIn 2017\, Liu and Montgomery proposed the study on the parameter $c_{\varepsilon}(G)$ which is the order of the smallest subgraph of $G$ with average degree at least $\varepsilon d(G)$. In fact\, they conjectured that for small enough $\varepsilon>0$\, every graph $G$ of average degree $d$ contains a clique subdivision of size $\Omega(\min\{d\, \sqrt{\frac{c_{\varepsilon}(G)}{\log c_{\varepsilon}(G)}}\})$. We prove that this conjecture holds up to a multiplicative $\min\{(\log\log d)^6\,(\log \log c_{\varepsilon}(G))^6\}$-term. \nAs a corollary\, for every graph $F$\, we determine the minimum size of the largest clique subdivision in $F$-free graphs with average degree $d$ up to multiplicative polylog$(d)$-term. \nThis is joint work with Jaehoon Kim\, Youngjin Kim\, and Hong Liu.
URL:https://dimag.ibs.re.kr/event/2021-11-30/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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