Bisimplicial vertices in even-hole-free graphs

Authors:
Louigi Addario-Berry;Maria Chudnovsky;Frédéric Havet;Bruce Reed;Paul Seymour
Affiliations:
McGill University, Montreal, Canada;Columbia University, New York, NY 10027, USA;Projet Mascotte, I3S (CNRS/UNSA)-INRIA, 2004 route des Lucioles, BP 93, 06902 Sophia-Antipolis Cedex, France;Canada Research Chair in Graph Theory, McGill University, Montreal, Canada and Projet MASCOTTE, Laboratoire IS3, CNRS, France;Princeton University, Princeton, NJ 08544, USA
Venue:
Journal of Combinatorial Theory Series B
Year:
2008

Citing 3
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Abstract

A hole in a graph is an induced subgraph which is a cycle of length at least four. A hole is called even if it has an even number of vertices. An even-hole-free graph is a graph with no even holes. A vertex of a graph is bisimplicial if the set of its neighbours is the union of two cliques. In this paper we prove that every even-hole-free graph has a bisimplicial vertex, which was originally conjectured by Reed.