On the stability number of claw-free P5-free and more general graphs Original Research Article

In this note we show that the stability number of a (4-pan, chair, K1, 4,P5)-free graph which has no simplicial vertex is bounded by 3. This generalizes the case of (claw, P5)-free graphs and leads to a very simple polynomial-time algorithm for determining the stability number of (claw, P5)-free graphs and, more generally, of (4-pan,chair, K1, 4, P5)-free graphs.