A class of perfectly contractile graphs

We consider the class A of graphs that contain no odd hole, no antihole, and no "prism" (a graph consisting of two disjoint triangles with three disjoint paths between them). We prove that every graph G A different from a clique has an "even pair" (two vertices that are not joined by a chordless path of odd length), as conjectured by Everett and Reed [see the chapter "Even pairs" in the book Perfect Graphs, J.L. Ram

• Type: Journal
• Year: 2006
• Where: JCT
• Authors: Frédéric Maffray, Nicolas Trotignon
• Keywords: Disjoint Paths, Disjoint Triangles, JCT 2006, Odd Hole