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Digraphs with the path‐merging property
Author(s) -
BangJensen Jørgen
Publication year - 1995
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190200214
Subject(s) - digraph , combinatorics , hamiltonian path , mathematics , path (computing) , disjoint sets , discrete mathematics , directed graph , graph , undirected graph , property (philosophy) , longest path problem , induced path , shortest path problem , computer science , epistemology , programming language , philosophy
In this paper we study those digraphs D for which every pair of internally disjoint ( X, Y )‐paths P 1 , P 2 can be merged into one ( X, Y )‐path P * such that V ( P 1 ) ∪ V ( P 2 ), 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.