Facets with fixed defect of the stable set polytope

Abstract.

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 ∑ _v∈V a(v)x _v ≤b of this polytope we associate an integer δ, called the defect of the facet, by δ=∑ _v∈V a(v)-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.