Claw-free graphs. II. Non-orientable prismatic graphs

A graph is prismatic if for every triangle T , every vertex not in T has exactly one neighbour in T . In a previous paper we gave a complete description of all 3-colourable prismatic graphs, and of a slightly more general class, the “orientable” prismatic graphs. In this paper we describe the non-orientable ones, thereby completing a description of all prismatic graphs. Since complements of prismatic graphs are claw-free, this is a step towards the main goal of this series of papers, providing a structural description of all claw-free graphs (a graph is claw-free if no vertex has three pairwise nonadjacent neighbours).