List matrix partitions of chordal graphs (original) (raw)

Abstract

It is well known that a clique with k + 1 vertices is the only minimal obstruction to k-colourability of chordal graphs. A similar result is known for the existence of a cover by cliques. Both of these problems are in fact partition problems, restricted to chordal graphs. The first seeks partitions into k independent sets, and the second is equivalent to finding partitions into cliques. In an earlier paper we proved that a chordal graph can be partitioned into k independent sets and cliques if and only if it does not contain an induced disjoint union of + 1 cliques of size k + 1. (A linear time algorithm for finding such partitions can be derived from the proof.)

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