New facets of the 2-dominating set polytope of trees

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.Sociedad Argentina de Informática e Investigación Operativ

New facets of the 2-dominating set polytope of trees

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.Sociedad Argentina de Informática e Investigación Operativ

New facets of the 2-dominating set polytope of trees

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.Sociedad Argentina de Informática e Investigación Operativ

On the Complexity of {k}-domination for Chordal Graphs

In this work we obtain a new graph class where {k}-DOM is NP-complete: the class of chordal graphs. We also identify some maximal subclasses for which it is polynomial time solvable. By relating this problem with k-DOM, we prove that {k}-DOM is polynomial time solvable for strongly chordal graphs. Besides, by expressing the property involved in k-DOM in Counting Monadic Second- order Logic, we obtain that both problems are linear time solvable for bounded tree-width graphs. In this way we enlarge the family of graphs for which k-DOM is polynomial time solvable.Sociedad Argentina de Informática e Investigación Operativ

Polyhedra associated with identifying codes

In this work we study the associated polyhedra and present some general results on their combinatorial structure. We demonstrate how the polyhedral approach can be applied to find minimum identifying codes for special bipartite graphs and cycles, and discuss further lines of research in order to obtain strong lower bounds stemming from linear relaxations of the identifying code polyhedron, enhanced by suitable cutting planes to be used in a B&C framework.Sociedad Argentina de Informática e Investigación Operativ

Polyhedral study of the 2-dominating set polytope of cycles and cactus graphs

Domination and its variations arise in many applications, in particular in those involving strategic placement of items at vertices of a network. For general graphs these problems are NP-hard, however, domination in graphs has been shown to be polynomially solvable in several graph classes. In this work we consider a generalization of this problem called k-domination in graphs.Sociedad Argentina de Informática e Investigación Operativ

On the Complexity of {k}-domination for Chordal Graphs

In this work we obtain a new graph class where {k}-DOM is NP-complete: the class of chordal graphs. We also identify some maximal subclasses for which it is polynomial time solvable. By relating this problem with k-DOM, we prove that {k}-DOM is polynomial time solvable for strongly chordal graphs. Besides, by expressing the property involved in k-DOM in Counting Monadic Second- order Logic, we obtain that both problems are linear time solvable for bounded tree-width graphs. In this way we enlarge the family of graphs for which k-DOM is polynomial time solvable.Sociedad Argentina de Informática e Investigación Operativ

On the Complexity of {k}-domination for Chordal Graphs

In this work we obtain a new graph class where {k}-DOM is NP-complete: the class of chordal graphs. We also identify some maximal subclasses for which it is polynomial time solvable. By relating this problem with k-DOM, we prove that {k}-DOM is polynomial time solvable for strongly chordal graphs. Besides, by expressing the property involved in k-DOM in Counting Monadic Second- order Logic, we obtain that both problems are linear time solvable for bounded tree-width graphs. In this way we enlarge the family of graphs for which k-DOM is polynomial time solvable.Sociedad Argentina de Informática e Investigación Operativ

Polyhedral study of the 2-dominating set polytope of cycles and cactus graphs

Domination and its variations arise in many applications, in particular in those involving strategic placement of items at vertices of a network. For general graphs these problems are NP-hard, however, domination in graphs has been shown to be polynomially solvable in several graph classes. In this work we consider a generalization of this problem called k-domination in graphs.Sociedad Argentina de Informática e Investigación Operativ

Polyhedra associated with identifying codes

In this work we study the associated polyhedra and present some general results on their combinatorial structure. We demonstrate how the polyhedral approach can be applied to find minimum identifying codes for special bipartite graphs and cycles, and discuss further lines of research in order to obtain strong lower bounds stemming from linear relaxations of the identifying code polyhedron, enhanced by suitable cutting planes to be used in a B&C framework.Sociedad Argentina de Informática e Investigación Operativ