Affiliation:
1. Department of Computer Science Institute of Theoretical Computer Science ETH Zürich Switzerland
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.
Funder
Eidgenössische Technische Hochschule Zürich
Subject
Geometry and Topology,Discrete Mathematics and Combinatorics