On the stable set problem in special P5-free graphs

Authors:
Michael U. Gerber;Vadim V. Lozin
Affiliations:
Department of Mathematics, Swiss Federal Institute of Technology EPFL, CH-1015 Lausanne, Switzerland;Department of Mathematics, Swiss Federal Institute of Technology EPFL, CH-1015 Lausanne, Switzerland
Venue:
Discrete Applied Mathematics
Year:
2003

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Abstract

The complexity status of the stable set problem in P5-free graphs remains an open question for a long time in spite of a lot of particular results in this direction. The purpose of the present paper is to summarize these results and to propose several new ones. In particular, we prove that the problem of finding a maximum stable set can be solved in polynomial time in the class of (P5,Km,m)-free graphs for any fixed m.