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Raphael Steiner, Congruence-constrained subdivisions in digraphs

Wednesday, August 31, 2022 @ 4:30 PM - 5:30 PM KST

Zoom ID: 869 4632 6610 (ibsdimag)

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.

[1] https://arxiv.org/abs/2208.06358

[2] https://arxiv.org/abs/2206.13635


Wednesday, August 31, 2022
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
대전 유성구 엑스포로 55 (우) 34126
IBS Discrete Mathematics Group (DIMAG)
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
E-mail: dimag@ibs.re.kr, Fax: +82-42-878-9209
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