2014/04/30 by Raffaele Mosca, Mosca, Raffaele
Computer Science · Mathematics · #52B12 (05C75) #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #cs.DM #math.CO #msc:52B12
paper · pdf · doi:10.48550/arxiv.1404.7623
arxiv created 2014/04/30 · arxiv updated 2014/05/01
The stable set polytope of a graph G, denoted as STAB(G), is the convex hull of all the incidence vectors of stable sets of G. To describe a linear system which defines STAB(G) seems to be a difficult task in the general case. In this paper we present a complete description of the stable set polytope of (P6,triangle)-free graphs (and more generally of (P6,paw)-free graphs). For that we combine different tools, in the context of a well known result of Chvátal \citeChvatal1975 which allows to focus just on prime facet-inducing graphs, with particular reference to a structure result on prime (P6,triangle)-free graphs due to Brandstädt et al. \citeBraKleMah2005. Also we point out some peculiarities of new facet-inducing graphs detected along this study with the help of a software.