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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.