Even Pairs in Claw-Free Perfect Graphs

  title={Even Pairs in Claw-Free Perfect Graphs},
  author={Cl{\'a}udia Linhares Sales and Fr{\'e}d{\'e}ric Maffray},
  journal={J. Comb. Theory, Ser. B},
An even pair in a graph is a pair of non-adjacent vertices such that every chordless path between them has even length. A graph is called strict quasi-parity when every induced subgraph that is not a clique has an even pair, and it is called perfectly contractile when every induced subgraph can be turned into a clique through a sequence of even-pair contractions. In this paper we determine the K1, 3-free graphs that are strict quasi-parity and those that are perfectly contractile. We show that… CONTINUE READING