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Characterizing and computing minimal cograph completions (Journal article)

Papadopoulos, C./ Lokshtanov, D./ Mancini, F.

A cograph completion of an arbitrary graph G is a cograph supergraph of G on the same vertex set. Such a completion is called minimal if the set of edges added to G is inclusion minimal. In this paper we present two results on minimal cograph completions. The first is a a characterization that allows us to check in linear time whether a given cograph completion is minimal. The second result is a vertex incremental algorithm to compute a minimal cograph completion H of an arbitrary input graph G in O(|V (H)| + |E(H)|) time.