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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:20220101T000000
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BEGIN:VEVENT
DTSTART;VALUE=DATE:20231101
DTEND;VALUE=DATE:20231106
DTSTAMP:20260418T193652
CREATED:20230911T044018Z
LAST-MODIFIED:20240705T161224Z
UID:7610-1698796800-1699228799@dimag.ibs.re.kr
SUMMARY:The 3rd East Asia Workshop on Extremal and Structural Graph Theory
DESCRIPTION:The 3rd East Asia Workshop on Extremal and Structural Graph Theory is a workshop to bring active researchers in the field of extremal and structural graph theory\, especially in the East Asia such as China\, Japan\, and Korea. \nWebsite: http://tgt.ynu.ac.jp/2023EastAsia.html
URL:https://dimag.ibs.re.kr/event/20231101/
LOCATION:The Southern Beach Hotel & Resort Okinawa
CATEGORIES:Workshops and Conferences
ORGANIZER;CN="Seog-Jin Kim (%EA%B9%80%EC%84%9D%EC%A7%84)":MAILTO:skim12@konkuk.ac.kr
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20231107T163000
DTEND;TZID=Asia/Seoul:20231107T173000
DTSTAMP:20260418T193652
CREATED:20230803T141247Z
LAST-MODIFIED:20240705T161256Z
UID:7449-1699374600-1699378200@dimag.ibs.re.kr
SUMMARY:Bruce A. Reed\, Some Variants of the Erdős-Sós Conjecture
DESCRIPTION:Determining the density required to ensure that a host graph G contains some target graph as a subgraph or minor is a natural and well-studied question in extremal combinatorics. The celebrated 50-year-old Erdős-Sós conjecture states that for every k\, if G has average degree exceeding k-2 then it contains every tree T with k vertices as a subgraph. This is tight as the clique with k-1 vertices contains no tree with k vertices as a subgraph. \nWe present some variants of this conjecture. We first consider replacing bounds on the average degree by bounds on the minimum and maximum degrees. We then consider replacing subgraph by minor in the statement.
URL:https://dimag.ibs.re.kr/event/2023-11-07/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20231120T163000
DTEND;TZID=Asia/Seoul:20231120T173000
DTSTAMP:20260418T193652
CREATED:20231031T024622Z
LAST-MODIFIED:20240707T072908Z
UID:7825-1700497800-1700501400@dimag.ibs.re.kr
SUMMARY:Seunghun Lee (이승훈)\, On colorings of hypergraphs embeddable in $\mathbb{R}^d$
DESCRIPTION:Given a hypergraph $H=(V\,E)$\, we say that $H$ is (weakly) $m$-colorable if there is a coloring $c:V\to [m]$ such that every hyperedge of $H$ is not monochromatic. The (weak) chromatic number of $H$\, denoted by $\chi(H)$\, is the smallest $m$ such that $H$ is $m$-colorable. A vertex subset $T \subseteq V$ is called a transversal of $H$ if for every hyperedge $e$ of $H$ we have $T\cap e \ne \emptyset$. The transversal number of $H$\, denoted by $\tau(H)$\, is the smallest size of a transversal in $H$. The transversal ratio of $H$ is the quantity $\tau(H)/|V|$ which is between 0 and 1. Since a lower bound on the transversal ratio of $H$ gives a lower bound on $\chi(H)$\, these two quantities are closely related to each other. \nUpon my previous presentation\, which is based on the joint work with Joseph Briggs and Michael Gene Dobbins (https://www.youtube.com/watch?v=WLY-8smtlGQ)\, we update what is discovered in the meantime about transversals and colororings of geometric hypergraphs. In particular\, we focus on chromatic numbers of $k$-uniform hypergraphs which are embeddable in $\mathbb{R}^d$ by varying $k$\, $d$\, and the notion of embeddability and present lower bound constructions. This result can also be regarded as an improvement upon the research program initiated by Heise\, Panagiotou\, Pikhurko\, and Taraz\, and the program by Lutz and Möller. We also present how this result is related to the previous results and open problems regarding transversal ratios. This presentation is based on the joint work with Eran Nevo.
URL:https://dimag.ibs.re.kr/event/2023-11-20/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20231128T163000
DTEND;TZID=Asia/Seoul:20231128T173000
DTSTAMP:20260418T193652
CREATED:20231031T121453Z
LAST-MODIFIED:20240707T072649Z
UID:7831-1701189000-1701192600@dimag.ibs.re.kr
SUMMARY:Hyunwoo Lee (이현우)\, Towards a high-dimensional Dirac's theorem
DESCRIPTION:Dirac’s theorem determines the sharp minimum degree threshold for graphs to contain perfect matchings and Hamiltonian cycles. There have been various attempts to generalize this theorem to hypergraphs with larger uniformity by considering hypergraph matchings and Hamiltonian cycles. \nWe consider another natural generalization of the perfect matchings\, Steiner triple systems. As a Steiner triple system can be viewed as a partition of pairs of vertices\, it is a natural high-dimensional analogue of a perfect matching in graphs. \nWe prove that for sufficiently large integer $n$ with $n \equiv 1 \text{ or } 3 \pmod{6}\,$ any $n$-vertex $3$-uniform hypergraph $H$ with minimum codegree at least $\left(\frac{3 + \sqrt{57}}{12} + o(1) \right)n = (0.879… + o(1))n$ contains a Steiner triple system. In fact\, we prove a stronger statement by considering transversal Steiner triple systems in a collection of hypergraphs. \nWe conjecture that the number $\frac{3 + \sqrt{57}}{12}$ can be replaced with $\frac{3}{4}$ which would provide an asymptotically tight high-dimensional generalization of Dirac’s theorem.
URL:https://dimag.ibs.re.kr/event/2023-11-28/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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