Decomposing Berge Graphs Containing No Proper Wheel, Long Prism Or Their Complements

In this paper we show that, if G is a Berge graph such that neither G nor its complement G contains certain induced subgraphs, named proper wheels and long prisms, then either G is a basic perfect graph (a bipartite graph, a line graph of a bipartite graph or the complement of such graphs) or it has a skew partition that cannot occur in a minimally imperfect graph. This structural result implies that G is perfect.

• Type: Journal
• Year: 2006
• Where: COMBINATORICA
• Authors: Michele Conforti, Gérard Cornuéjols, Giacomo Zambelli
• Keywords: Basic Perfect Graph, Berge Graph, Bipartite Graph, COMBINATORICA 2006