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X-WR-CALDESC:Events for Discrete Mathematics Group
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TZID:Asia/Seoul
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TZOFFSETFROM:+0900
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DTSTART:20210101T000000
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DTSTART;TZID=Asia/Seoul:20220113T163000
DTEND;TZID=Asia/Seoul:20220113T173000
DTSTAMP:20260419T200830
CREATED:20220113T073000Z
LAST-MODIFIED:20240707T080528Z
UID:5009-1642091400-1642095000@dimag.ibs.re.kr
SUMMARY:Ron Aharoni\, A strong version of the Caccetta-Haggkvist conjecture
DESCRIPTION:The Caccetta-Haggkvist conjecture\, one of the best known in graph theory\, is that in a digraph with $n$ vertices in which all outdegrees are at least $n/k$ there is a directed cycle of length at most $k$. This is known for  large values of $k$\, relatively to n\, and asymptotically for n large. A few years ago I offered a generalization: given sets $F_1$\, $\ldots$\, $F_n$ of sets of undirected edges\, each of size at least $n/k$\, there exists a rainbow undirected cycle of length  at most $k$. The directed version is obtained by taking as $F_i$ the set of edges going out of the vertex $v_i$ ($i \le n$)\, with the directions removed. I will tell about recent results on this conjecture\, obtained together with He Guo\, with Beger\, Chudnovsky and Zerbib\, and with DeVos and Holzman.
URL:https://dimag.ibs.re.kr/event/2022-01-13/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
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