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

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 Open Locating-Dominating and Locating Total-Dominating Sets in Graphs

International audienceThe problems of determining open locating-dominating or locating total-dominating sets of minimum cardinality in a graph G are variations of the classical minimum dominating set problem in G and are all known to be hard for general graphs. A typical line of attack is therefore to determine the cardinality of minimum such sets in special graphs. In this work we study the two problems from a polyhedral point of view. We provide the according linear relaxations, discuss their combinatorial structure, and demonstrate how the associated polyhedra can be entirely described or polyhedral arguments can be applied to find minimum such sets for special graphs

Locating-Domination and Identification

International audienceLocating-domination and identification are two particular, related, types of domination: a set C of vertices in a graph G = (V, E) is a locating-dominating code if it is dominating and any two vertices of V \ C are dominated by distinct sets of codewords; C is an identifying code if it is dominating and any two vertices of V are dominated by distinct sets of codewords. This chapter presents a survey of the major results on locating-domination and on identification