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Ron Aharoni, A strong version of the Caccetta-Haggkvist conjecture

January 13 Thursday @ 4:30 PM - 5:30 PM KST

Zoom ID: 869 4632 6610 (ibsdimag)


Ron Aharoni
Department of Mathematics, Technion

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.


January 13 Thursday
4:30 PM - 5:30 PM KST
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Zoom ID: 869 4632 6610 (ibsdimag)


O-joung Kwon (권오정)
IBS 이산수학그룹 Discrete Mathematics Group
기초과학연구원 수리및계산과학연구단 이산수학그룹
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IBS Discrete Mathematics Group (DIMAG)
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