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DTSTART:20210101T000000
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DTSTART;TZID=Asia/Seoul:20220118T163000
DTEND;TZID=Asia/Seoul:20220118T173000
DTSTAMP:20260424T014113
CREATED:20220118T073000Z
LAST-MODIFIED:20240707T080518Z
UID:5105-1642523400-1642527000@dimag.ibs.re.kr
SUMMARY:Jaehyeon Seo (서재현)\, A rainbow Turán problem for color-critical graphs
DESCRIPTION:For given $k$ graphs $G_1\,\dots\, G_k$ over a common vertex set of size $n$\, what conditions on $G_i$ ensures a ‘colorful’ copy of $H$\, i.e. a copy of $H$ containing at most one edge from each $G_i$? \nKeevash\, Saks\, Sudakov\, and Verstraëte defined $\operatorname{ex}_k(n\,H)$ to be the maximum total number of edges of the graphs $G_1\,\dots\, G_k$ on a common vertex set of size $n$ having no colorful copy of $H$. They completely determined $\operatorname{ex}_k(n\,K_r)$ for large $n$ by showing that\, depending on the value of $k$\, one of the two natural constructions is always the extremal construction. Moreover\, they conjectured the same holds for every color-critical graphs and proved it for $3$-color-critical graphs. \nWe prove their conjecture for $4$-color-critical graphs and for almost all $r$-color-critical graphs when $r > 4$. Moreover\, we show that for every non-color-critical non-bipartite graphs\, none of the two natural constructions is extremal for certain values of $k$. This is a joint work with Debsoumya Chakraborti\, Jaehoon Kim\, Hyunwoo Lee\, and Hong Liu.
URL:https://dimag.ibs.re.kr/event/2022-01-18/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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