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

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

2008-03-14

arxiv.org/abs/0803.2135v1

Computer Science

Discrete Mathematics

Scientific paper

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 obtain some 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 have bounded clique-width.

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