Regular Article: Bi-complement Reducible Graphs

Authors:
Vassilis Giakoumakis;Jean-Marie Vanherpe
Affiliations:
LaRIA Université de Picardie Jules Verne, CURI 5 rue du Moulin Neuf, 80000, Amiens, France;LaRIA Université de Picardie Jules Verne, CURI 5 rue du Moulin Neuf, 80000, Amiens, France
Venue:
Advances in Applied Mathematics
Year:
1997

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Abstract

We introduce a new family of bipartite graphs which is the bipartite analogue of the class ofcomplement reduciblegraphs orcographs. Abi-complement reduciblegraph orbi-cographis a bipartite graphG=(W@?B,E) that can be reduced to single vertices by recursively bi-complementing the edge set of all connected bipartite subgraphs. Thebi-complementedgraphG@?^b^i^pofGis the graph having the same vertex setW@?BasG, while its edge set is equal toWxB-E. The aim of this paper is to show that there exists an equivalent definition of bi-cographs by three forbidden configurations. We also propose a tree representation for this class of graphs.