DIGRAPHS WITH THE PATH-MERGING PROPERTY

In this paper we study those digraphs D for which every pair of intern ally disjoint (x, y)-paths P-1, P-2 can be merged into one (x, y)-path P such that V(P*) = V(P-1) boolean OR V(P-2), for every choice of ve rtices x, y is an element of V(D). We call this property the path-merg ing property and we call a graph path-mergeable if it has the path-mer ging property. We show that each such digraph has a directed hamiltoni an cycle whenever it can possibly have one, i.e., it is strong and the underlying graph has no cutvertex. We show that path-mergeable digrap hs can be recognized in polynomial time and we give examples of large classes of such digraphs which are not contained in any previously stu died class of digraphs. We also discuss which undirected graphs have p ath-mergeable digraph orientations. (C) 1995 John Wiley & Sons, Inc.