Excluding 4-Wheels


  • Partially supported by Agence Nationale de la Recherche under reference anr 10 jcjc 0204 01.


A 4-wheel is a graph formed by a cycle C and a vertex not in C that has at least four neighbors in C. We prove that a graph G that does not contain a 4-wheel as a subgraph is 4-colorable and we describe some structural properties of such a graph.