Bipartite-perfect graphs (Q1811078)

Two graphs \(G\) and \(H\) on the vertex set \(V\) are \(P_4\)-isomorphic if there is a permutation \(\pi\) on \(V\) such that, for all subsets \(S\) of \(V\), \(S\) induces a chordless \(P_4\) in \(G\) if and only if \(\pi (S)\) induces a \(P_4\) in \(H\). The author characterizes all graphs \(P_4\)-isomorphic to a bipartite graph. For example, we can derive from such a graph or its complement a bipartite graph, or a tree-perfect graph, or two particular graphs on 7 and 8 vertices. The proof requires an exhaustive examination of the possible neighbors of the vertices in known cycles.