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X-WR-CALDESC:Events for Discrete Mathematics Group
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TZID:Asia/Seoul
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DTSTART:20190101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20200714T163000
DTEND;TZID=Asia/Seoul:20200714T173000
DTSTAMP:20260420T031734
CREATED:20200708T123817Z
LAST-MODIFIED:20240707T083801Z
UID:2622-1594744200-1594747800@dimag.ibs.re.kr
SUMMARY:Casey Tompkins\, Inverse Turán Problems
DESCRIPTION:For given graphs $G$ and $F$\, the Turán number $ex(G\,F)$ is defined to be the maximum number of edges in an $F$-free subgraph of $G$. Briggs and Cox introduced a dual version of this problem wherein for a given number $k$\, one maximizes the number of edges in a host graph $G$ for which $ex(G\,H) < k$.  We resolve a problem of Briggs and Cox in the negative by showing that the inverse Turán number of $C_4$ is $\Theta(k^{3/2})$. More generally\, we determine the order of magnitude of the inverse Turán number of $K_{s\,t}$ for all $s$ and $t$.  Addressing another problem of Briggs and Cox\, we determine the asymptotic value of the inverse Turán number of the paths of length $4$ and $5$ and provide an improved lower bound for all paths of even length.  We also obtain improved bounds on the inverse Turán number of even cycles \nJoint work with Ervin Győri\, Nika Salia and Oscar Zamora.
URL:https://dimag.ibs.re.kr/event/2020-07-14/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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