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X-WR-CALDESC:Events for Discrete Mathematics Group
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TZOFFSETFROM:+0900
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DTSTART:20220101T000000
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DTSTART;TZID=Asia/Seoul:20230516T163000
DTEND;TZID=Asia/Seoul:20230516T173000
DTSTAMP:20260419T080043
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
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