Opposition graphs are strict quasi-parity graphs

Abstract

An opposition graph is a graph whose edges can be acyclically oriented in such a way that every chordless path on four vertices has its extreme edges both pointing in or pointing out. A strict quasi-parity graph is a graphG such that every induced subgraphH ofG either is a clique or else contains a pair of vertices which are not endpoints of an odd (number of edges) chordless path ofH. The perfection of opposition graphs and strict quasi-parity graphs was established respectively by Olariu and Meyniel. We show here that opposition graphs are strict quasi-parity graphs.