da Silva, MV and Vuskovic, K (2007) Triangulated neighborhoods in even-hole-free graphs. Discrete Mathematics, 307 (9-10). 1065 - 1073 . ISSN 0012-365X
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.
|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:||29 Oct 2016 07:03|