We extend the notion of P4-sparse graphs previously introduced by {\scshape Ho\`ang} by considering F-sparse graphs were F denotes a finite set of graphs on p vertices. Thus we obtain some results on (P5,P5ˉ)-sparse graphs already known on (P5,P5ˉ)-free graphs. Finally we completely describe the structure of (P5,P5ˉ,bull)-sparse graphs, it follows that those graphs have bounded clique-width.
@article{arxiv.0803.2135,
title = {On $(P_5,\bar{P_5})$-sparse graphs and other families},
author = {Jean-Luc Fouquet and Jean-Marie Vanherpe},
journal= {arXiv preprint arXiv:0803.2135},
year = {2008}
}