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 Sigma(v is an element of V) a(v)x(v) less than or equal to b of this polytope we associate an integer delta, called the defect of the facet, by delta = Sigma(v is an element of V) a(v) - 2b. We show that for any fixed delta there is a finite collection of graphs (called "basis") such that any graph with a facet of defect delta contains a subgraph which can be obtained from one of the graphs in the basis by a simple subdivision operation.