Article ID Journal Published Year Pages File Type
4648923 Discrete Mathematics 2007 9 Pages PDF
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+2mn+2m maximal cliques. It also yields an O(n2m)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.

Related Topics
Physical Sciences and Engineering Mathematics Discrete Mathematics and Combinatorics
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