On the k-dominating set polytope of web graphs

Abstract In this work we present some results on the polyhedral structure of the convex hull of integer points in polyhedra of the form { x ⩾ 0 : M x ⩾ k 1 } , for a 0, 1 matrix M and a positive integer number k. In particular, we consider the k-dominating set problem in a graph. Given a graph G = ( V , E ) , a set D ⊆ V is a k-dominating set if every vertex in V is adjacent to at least k vertices of D. The k-dominating set problem consists in finding a k-dominating set of minimum cardinality. The k-dominating set polytope is the convex hull of the incidence vectors of k-dominating sets in G and it is a natural generalization of the well-known dominating set polytope of a graph. We apply our results for general problems to the k-dominating set polytope of some particular families of web graphs.