Minimal obstructions for a matrix partition problem in chordal graphs

Abstract

In this article we consider graph partitions with prescribed patterns. Specifically we consider a 2-colouring of the vertex set of a graph such that one colour induces an independent set and the other colour induces a complete bipartite graph. We determine the complete list of obstructions (minimal forbidden induced subgraphs) for chordal graphs. This result completes the knowledge on minimal obstructions for 3 × 3 matrix partition problems on chordal graphs.