Characterizing and Computing Minimal Cograph Completions

Authors:
Daniel Lokshtanov;Federico Mancini;Charis Papadopoulos
Affiliations:
Department of Informatics, University of Bergen, Bergen, Norway N-5020;Department of Informatics, University of Bergen, Bergen, Norway N-5020;Department of Informatics, University of Bergen, Bergen, Norway N-5020
Venue:
FAW '08 Proceedings of the 2nd annual international workshop on Frontiers in Algorithmics
Year:
2008

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Abstract

A cograph completion of an arbitrary graph Gis a cograph supergraph of Gon the same vertex set. Such a completion is called minimal if the set of edges added to Gis 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 Hof an arbitrary input graph Gin O(V(H) + E(H)) time.