Minimal interval completions

Abstract

We study the problem of adding edges to an arbitrary graph so that the resulting graph is an interval graph. Our objective is to add an inclusion minimal set of edges, which means that no proper subset of the added edges can result in an interval graph when added to the original graph. We give a polynomial time algorithm to obtain a minimal interval completion of an arbitrary graph, thereby resolving the complexity of this problem. © Springer-Verlag Berlin Heidelberg 2005.