ON THE P4-STRUCTURE OF PERFECT GRAPHS .4. PARTNER GRAPHS

Two vertices x, y of a graph G are called partners if there exist vertices u, v, w distinct from x, y such that {x, u, v, w} and {y, u, v, w} each induce a chordless path in G. The partner graph of G is the graph whose vertices are the vertices of G and whose edges are partners in G. The partner graph of G is completely determined by the P4-structure of G. We show that the Strong Perfect Graph Conjecture holds for graphs with triangle-free partner graphs. © 1990.