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PRODID:-//Discrete Mathematics Group - ECPv6.15.20//NONSGML v1.0//EN
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X-WR-CALDESC:Events for Discrete Mathematics Group
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TZID:Asia/Seoul
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DTSTART:20180101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20191212T163000
DTEND;TZID=Asia/Seoul:20191212T173000
DTSTAMP:20260420T165112
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
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