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On $(P_5,\bar{P_5})$-sparse graphs and other families (0803.2135v1)
Published 14 Mar 2008 in cs.DM
Abstract: 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.