On the Dominating Set Polytope of a Cycle
نویسنده
چکیده
A subset of vertices of a graph is called a dominating set if every vertex of the graph which is not present in the set has at least one neighbour in it. Dominating set polytope of a graph is defined as the convex hull of 0/1-incidence vectors of all the dominating sets of the graph. This paper presents complete characterization of the dominating set polytope of a cycle.
منابع مشابه
On the independent dominating set polytope
In this paper, we consider the independent dominating set polytope. We give a complete linear description of that polytope when the graph is reduced to a cycle. This description uses a general class of valid inequalities introduced in [T.M. Contenza, Some results on the dominating set polytope, Ph.D. Dissertation, University of Kentucky, 2000]. We devise a polynomial time separation algorithm f...
متن کاملOn independent domination numbers of grid and toroidal grid directed graphs
A subset $S$ of vertex set $V(D)$ is an {em indpendent dominating set} of $D$ if $S$ is both an independent and a dominating set of $D$. The {em indpendent domination number}, $i(D)$ is the cardinality of the smallest independent dominating set of $D$. In this paper we calculate the independent domination number of the { em cartesian product} of two {em directed paths} $P_m$ and $P_n$ for arbi...
متن کاملSimple Extended Formulation for the Dominating Set Polytope via Facility Location
In this paper we present an extended formulation for the dominating set polytope via facility location. We show that with this formulation we may describe the dominating set polytope for some class of graphs as cacti graphs, though its description in the natural node variables dimension has been only partially obtained. Moreover, the inequalities describing this polytope have coefficients in {−...
متن کاملPolyhedral studies in Domination Graph Theory (I)
This paper discusses polyhedral approaches to problems in Domination Graph Thoery. We give various linear integer programming formulations for the weighted and unweighted versions of the minimum dominating set problem. We study the associated polytopes and determine dimension of the polytopes, facets, valid inequalities et al. Ideas from integer programming such as lift and project are used to ...
متن کاملSome Results on the Maximal 2-Rainbow Domination Number in Graphs
A 2-rainbow dominating function ( ) of a graph is a function from the vertex set to the set of all subsets of the set such that for any vertex with the condition is fulfilled, where is the open neighborhood of . A maximal 2-rainbow dominating function on a graph is a 2-rainbow dominating function such that the set is not a dominating set of . The weight of a maximal is the value . ...
متن کامل