On Planar Perfectly Contractile Graphs

Abstract

An even pair in a graph is a pair of vertices such that every chordless path between them has even length. A graph is called perfectly contractile when every induced subgraph can be transformed into a clique through a sequence of even-pair contractions. In this paper we characterize the planar graphs that are perfectly contractile by determining all the minimal forbidden subgraphs. We give a polynomial algorithm for the recognition of perfectly contractile planar graphs.