Facets with fixed defect of the stable set polytope

The stable set polytope of a graph is the convex hull of the 0–1 vectors corresponding to stable sets of vertices. To any nontrivial facet Σν∈Va(ν)xν ≤ b of this polytope we associate an integer δ, called the defect of the facet, by δ = Σν∈Va(ν) – 2b. We show that for any fixed δ there is a finite collection of graphs (called ‘basis’) such that any graph with a facet of defect δ contains a subgraph which can be obtained from one of the graphs in the basis by a simple subdivision operation.