Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4648923 | Discrete Mathematics | 2007 | 9 Pages |
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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Murilo V.G. da Silva, Kristina Vušković,