Triangulated neighborhoods in even-hole-free graphs

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(n2 m) 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.

• Type: Journal
• Year: 2007
• Where: DM
• Authors: Murilo Vicente Gonçalves da Silva, Kristina Vuskovic
• Keywords: Chordless Cycle, DM 2007, Even-hole-free Graphs, Triangulated