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Triangulated neighborhoods in even-hole-free graphs

da Silva, MV and Vuskovic, K (2007) Triangulated neighborhoods in even-hole-free graphs. Discrete Mathematics, 307 (9-10). 1065 - 1073 . ISSN 0012-365X

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Abstract

An even-hole-free graph is a graph that does not contain, as an induced subgraph, a chordless cycle of even length. A graph is triangulated if it does not contain any chordless cycle of length greater than three, as an induced subgraph. We prove that every even-hole-free graph has a node whose neighborhood is triangulated. This implies that in an even-hole-free graph, with n nodes and m edges, there are at most n+2m maximal cliques. It also yields an O(n2m) algorithm that generates all maximal cliques of an even-hole-free graph. In fact these results are obtained for a larger class of graphs that contains even-hole-free graphs.

Item Type: Article
Copyright, Publisher and Additional Information: © 2007, Elsevier. This is an author produced version of a paper published in Discrete Mathematics. Uploaded in accordance with the publisher's self-archiving policy.
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds)
Depositing User: Symplectic Publications
Date Deposited: 18 Jun 2012 15:33
Last Modified: 09 Jun 2014 10:45
Published Version: http://dx.doi.org/10.1016/j.disc.2006.07.027
Status: Published
Publisher: Elsevier
Identification Number: 10.1016/j.disc.2006.07.027
URI: http://eprints.whiterose.ac.uk/id/eprint/74353

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