Characterizing Minimal Interval Completions
Abstract
Minimal interval completions of graphs are central in understanding two important and widely studied graph parameters: profile and pathwidth. Such understanding seems necessary to be able to attack the problem of computing these parameters. An interval completion of a given graph is an interval supergraph of it on the same vertex set, obtained by adding edges. If no subset of the added edges can be removed without destroying the interval property, we call it a minimal interval completion. In this paper, we give the first characterization of minimal interval completions. We present a polynomial time algorithm, for deciding whether a given interval completion of an arbitrary graph is minimal. If the interval completion is not minimal the algorithm can be used to extract a minimal interval completion that is a subgraph of the given interval completion.