Tree- and forest-perfect graphs

Two graphs G and H with the same vertex set V are P-4-isomorphic if there e xists a permutation pi on V such that, for all subsets S subset of or equal to V, S induces a chordless path on four vertices (denoted by P-4) in G if and only if pi(S) induces a P-4 in H. This paper gives a classification of all graphs P-4-isomorphic to a tree, respectively, a forest. (C) 1999 Else vier Science B.V. All rights reserved.