Subdivisions with congruence constraints in digraphs of large chromatic number

Abstract

AbstractWe prove that for every digraph and every assignment of pairs of integers to its arcs there exists an integer such that every digraph with dichromatic number greater than contains a subdivision of in which is subdivided into a directed path of length congruent to modulo , for every . 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.