English

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

Discrete Mathematics 2008-12-18 v1

Abstract

We extend the notion of P4P_4-sparse graphs previously introduced by {\scshape Ho\`ang} by considering F\mathcal{F}-sparse graphs were F\mathcal{F} denotes a finite set of graphs on pp vertices. Thus we obtain some results on (P5,P5ˉ)(P_5,\bar{P_5})-sparse graphs already known on (P5,P5ˉ)(P_5,\bar{P_5})-free graphs. Finally we completely describe the structure of (P5,P5ˉ,bull(P_5,\bar{P_5}, bull)-sparse graphs, it follows that those graphs have bounded clique-width.

Keywords

Cite

@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}
}