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

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

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

The role of leptin in the respiratory system: an overview

Since its cloning in 1994, leptin has emerged in the literature as a pleiotropic hormone whose actions extend from immune system homeostasis to reproduction and angiogenesis. Recent investigations have identified the lung as a leptin responsive and producing organ, while extensive research has been published concerning the role of leptin in the respiratory system. Animal studies have provided evidence indicating that leptin is a stimulant of ventilation, whereas researchers have proposed an important role for leptin in lung maturation and development. Studies further suggest a significant impact of leptin on specific respiratory diseases, including obstructive sleep apnoea-hypopnoea syndrome, asthma, COPD and lung cancer. However, as new investigations are under way, the picture is becoming more complex. The scope of this review is to decode the existing data concerning the actions of leptin in the lung and provide a detailed description of leptin's involvement in the most common disorders of the respiratory system

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

The identifying code, the locating-dominating, the open locating-dominating and the locating total-dominating problems under some graph operations

International audienceThe problems of determining minimum identifying, locating-dominating, open locating-dominating or locating total-dominating codes 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 codes in special graphs. In this work we study the change of minimum such codes under three operations in graphs: adding a universal vertex, taking the generalized corona of a graph, and taking the square of a graph. We apply these operations to paths and cycles which allows us to provide minimum codes in most of the resulting graph classes