Linear-time certifying recognition algorithms and forbidden induced subgraphs

Authors:
Pinar Heggernes;Dieter Kratsch
Affiliations:
Department of Informatics, University of Bergen, Bergen, Norway;Laboratoire d'Informatique Théorique et Appliquée Université Paul Verlaine-Metz, Metz Cedex 01, France
Venue:
Nordic Journal of Computing
Year:
2007

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Abstract

We give the first linear-time certifying algorithms to recognize split graphs, threshold graphs, chain graphs, co-chain graphs and trivially perfect graphs, with sublinear certificates for negative output. In case of membership in a given graph class our algorithms provide as certificate a structure for the input graph that characterizes the class, and in case of non-membership they provide as certificate a forbidden induced subgraph of the class. The certificates of membership can be authenticated in time O(n + m) and the certificates of non-membership can be authenticated in time O(1).