Minimal Interval Completions

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. This problem is closely related to the problem of adding an inclusion minimal set of edges to a graph to obtain a chordal graph, which is a well studied problem and which motivates an analogous study of minimal interval completions. However, whereas there are nice properties that result in efficient algorithms for obtaining a chordal graph in this way, the same problem for obtaining an interval graph is more difficult, and its computational complexity has been open until now. In this paper we give a polynomial time algorithm to obtain a minimal interval completion of an arbitrary graph, thereby resolving the complexity of this problem.

• Type: Conference
• Year: 2005
• Where: ESA
• Authors: Pinar Heggernes, Karol Suchan, Ioan Todinca, Yngve Villanger
• Keywords: Arbitrary Graph, ESA 2005, Inclusion Minimal Set, Interval Graph