2022/08/12 by Steiner, Raphael · 1 citation
#05C10 #05C15 #05C20 #05C38 #05C83 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2208.06358
We prove that for every digraph F and every assignment of pairs of integers (re,qe)e ∈ 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 re modulo qe, for every e ∈ A(F). This generalizes to the directed setting the analogous result by Thomassen for undirected graphs, and at the same time yields a novel short proof of his result.