Bipartite-perfect graphs Original Research Article

Two graphs G and H with the same vertex set V are P4-isomorphic if there exists a permutation π on V such that, for all subsets S⊆V, S induces a chordless path on four vertices (denoted by P4) in G if and only if π(S) induces a P4 in H. This paper gives a characterization of all graphs P4-isomorphic to a bipartite graph, which we call bipartite-perfect graphs. The characterization is based on graphs P4-isomorphic to a tree previously described by A. Brandstädt and the author, and implies a linear time recognition algorithm for bipartite-perfect graphs.