On 2-subcolourings of chordal graphs

Abstract

A 2-subcolouring of a graph is a partition of the vertices into two subsets, each inducing a P 3-free graph, i.e., a disjoint union of cliques. We give the first polynomial time algorithm to test whether a chordal graph has a 2-subcolouring. This solves (for two colours) an open problem of Broersma, Fomin, Nešetřil, and Woeginger, who gave an O(n 5) time algorithm for interval graphs. Our algorithm for the larger class of chordal graphs has complexity only O(n 3)