Characterizing Directed Path Graphs by Forbidden Asteroids - LIRMM - Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier
Article Dans Une Revue Journal of Graph Theory Année : 2011

Characterizing Directed Path Graphs by Forbidden Asteroids

Résumé

An asteroidal triple is a stable set of three vertices such that each pair is connected by a path avoiding the neighborhood of the third vertex. Asteroidal triples play a central role in a classical characterization of interval graphs by Lekkerkerker and Boland. Their result says that a chordal graph is an interval graph if and only if it does not contain an asteroidal triple. In this paper, we prove an analogous theorem for directed path graphs which are the intersection graphs of directed paths in a directed tree. For this purpose, we introduce the notion of a special connection. Two non-adjacent vertices are linked by a special connection if either they have a common neighbor or they are the endpoints of two vertex-disjoint chordless paths satisfying certain conditions. A special asteroidal triple is an asteroidal triple such that each pair is linked by a special connection. We prove that a chordal graph is a directed path graph if and only if it does not contain a special asteroidal triple.

Dates et versions

lirmm-00627742 , version 1 (29-09-2011)

Identifiants

Citer

Kathie Cameron, Chinh T. Hoàng, Benjamin Lévêque. Characterizing Directed Path Graphs by Forbidden Asteroids. Journal of Graph Theory, 2011, 68, pp.103-112. ⟨10.1002/jgt.20543⟩. ⟨lirmm-00627742⟩
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