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

Authors:
Maria Chudnovsky;Paul Seymour
Affiliations:
Columbia University, New York, NY 10027, USA;Princeton University, Princeton, NJ 08544, USA
Venue:
Journal of Combinatorial Theory Series B
Year:
2008

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Abstract

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).