On total [formula omitted]-domination: Polyhedral and algorithmic results

Abstract

Given a graph G=(V,E) and integer values fv, v∈V, a node subset D⊂V is a total f-dominating set if every node v∈V is adjacent to at least fv nodes of D. Given a weight system c(v), v∈V, the minimum weight total f-dominating set problem is to find a total f-dominating set of minimum total weight. In this article, we propose a polyhedral study of the associated polytope together with a complete and compact description of the polytope for totally unimodular graphs and cycles. We also propose a linear time dynamic programming algorithm for the case of trees.