New facets of the 2-dominating set polytope of trees

Abstract

Given a graph G and a nonnegative integer number k, a k- dominating set in G is a subset of vertices D such that every vertex in the graph is adjacent to at least k elements of D. The k-dominating set polytope is the convex hull of the incidence vectors of k-dominating sets in G. This is a natural generalization of the well-known dominating set polytope in graphs. In this work we study the 2-dominating set polytope of trees and we will provide new facet de ning inequalities for it.