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We extend the notion of $P_4$-sparse graphs previously introduced by{\scshape Ho\`ang} by considering $\mathcal{F}$-sparse graphs were$\mathcal{F}$ denotes a finite set of graphs on $p$ vertices. Thus we obtainsome results on $(P_5,\bar{P_5})$-sparse graphs already known on$(P_5,\bar{P_5})$-free graphs. Finally we completely describe the structure of$(P_5,\bar{P_5}, bull$)-sparse graphs, it follows that those graphs havebounded clique-width.

On $(P_5,\bar{P_5})$-sparse graphs and other families