Stable sets in two subclasses of banner-free graphs

Authors:
Michael U. Gerber;Alain Hertz;Vadim V. Lozin
Affiliations:
Department of Mathematics, Swiss Federal Institute of Technology, Lausanne, Switzerland;GERAD and Ecole Polytechnique, Montreal, Canada H3T 2A7;RUTCOR, Rutgers University, 640 Bartholomew Rd. Piscataway, NJ
Venue:
Discrete Applied Mathematics - Special issue on stability in graphs and related topics
Year:
2003

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Abstract

The maximum stable set problem is NP-hard, even when restricted to banner-free graphs. In this paper, we use the augmenting graph approach to attack the problem in two subclasses of banner-free graphs. We first provide both classes with the complete characterization of minimal augmenting graphs. Based on the obtained characterization, we prove polynomial solvability of the problem in the class of (banner, P8)-free graphs, improving several existing results.