On -sparse graphs and other families: Extended abstract

We extend the notion of P4-sparse graphs previously introduced by Hoàng in [C.T. Hoàng. Perfect Graphs, PhD thesis, School of Computer Science, McGill University, Montreal, 1985] by considering F -sparse graphs were F denotes a finite set of graphs on p vertices. Thus we obtain some results on ( P 5 , P ¯ 5 ) -sparse graphs already known on ( P 5 , P ¯ 5 ) -free graphs. Finally we completely describe the structure of ( P 5 , P ¯ 5 , bull ) -sparse graphs, it follows that those graphs have bounded clique-width.