A Strengthening of Ben Rebea′s Lemma

In this note we present a strengthening of a lemma due to A. Ben Rebea and used by V. Chvátal and N. Sbihi for the recognition of claw-free perfect graphs. We show that a claw-free graph with stability number at least four has no induced subgraph isomorphic to a C2p+1 with p ≥ 3. As a by-product we show that every vertex in a claw-free graph with stability number at least three is such that its neighbourhoodcan be covered by two complete graphs or contains an induced C5.