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

Jean-Luc Fouquet (1) , Jean-Marie Vanherpe (1)

1 LIFO - Laboratoire d'Informatique Fondamentale d'Orléans

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

Domaines: Mathématique discrète [cs.DM]

Jean-Luc Fouquet, Jean-Marie Vanherpe. On $(P_5,\overline{P_5})$-sparse graphs and other families. 2008. ⟨hal-00264104⟩