Abstract
AbstractIn this paper we study those digraphs D for which every pair of internally disjoint (X, Y)‐paths P1, P2 can be merged into one (X, Y)‐path P* such that V(P1) ∪ V(P2), for every choice of vertices X, Y ϵ V(D). We call this property the path‐merging property and we call a graph path‐mergeable if it has the path‐merging property. We show that each such digraph has a directed hamiltonian cycle whenever it can possibly have one, i.e., it is strong and the underlying graph has no cutvertex. We show that path‐mergeable digraphs can be recognized in polynomial time and we give examples of large classes of such digraphs which are not contained in any previously studied class of digraphs. We also discuss which undirected graphs have path‐mergeable digraph orientations. © 1995, John Wiley & Sons, Inc.
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