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DTSTART;TZID=Asia/Seoul:20220831T163000
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CREATED:20220816T233139Z
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UID:6033-1661963400-1661967000@dimag.ibs.re.kr
SUMMARY:Raphael Steiner\, Congruence-constrained subdivisions in digraphs
DESCRIPTION:I will present the short proof from [1] that for every digraph F and every assignment of pairs of integers $(r_e\,q_e)_{e\in A(F)}$ to its arcs\, there exists an integer $N$ such that every digraph D with dichromatic number at least $N$ contains a subdivision of $F$ in which $e$ is subdivided into a directed path of length congruent to $r_e$ modulo $q_e$ for every $e \in  A(F)$. This generalizes to the directed setting the analogous result by Thomassen for undirected graphs and at the same time yields a novel proof of his result. I will also talk about how a hypergraph coloring result from [2] may help to obtain good bounds on $N$ in the special case when $F$ is subcubic. \n[1] https://arxiv.org/abs/2208.06358 \n[2] https://arxiv.org/abs/2206.13635
URL:https://dimag.ibs.re.kr/event/2022-08-31/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
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