On Planar Quasi-Parity Graphs

A graph G is strict quasi parity (SQP) if every induced subgraph of G that is not a clique contains a pair of vertices with no odd chordless path between them (an even pair). Hougardy conjectured that the minimal forbidden subgraphs for the class of SQP graphs are the odd chordless cycles, the complements of odd or even chordless cycles, and some line-graphs of bipartite graphs. Here we prove this conjecture for planar graphs. We also give a constructive characterization of all the planar minimal forbidden subgraphs for the class of SQP graphs. Key words. perfect graphs, even pairs, planar graphs AMS subject classifications. 68R10, 68Q25, 05C85, 05C17, 90C27 DOI. 10.1137/060672649

• Type: Journal
• Year: 2008
• Where: SIAMDM
• Authors: Cláudia Linhares Sales, Frédéric Maffray, Bruce A. Reed
• Keywords: Minimal Forbidden Subgraphs, SIAMDM 2008, SQP Graphs, Strict Quasi Parity