On dart-free perfectly contractile graphs

Abstract

The dart is the five-vertex graph with degrees 4, 3, 2, 2, 1. An even pair is pair of vertices such that every chordless path between them has even length. A graph is perfectly contractile if every induced subgraph has a sequence of even-pair contractions that leads to a clique. We show that a recent conjecture on the forbidden structures for perfectly contractile graphs is satisfied in the case of dart-free graphs. Our proof yields a polynomial-time algorithm to recognize dart-free perfectly contractile graphs. © Springer-Verlag Berlin Heidelberg 2000.