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 the Dominating Set Polytope of a Cycle
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.
متن کاملSemidefinite relaxation for dominating set
‎It is a well-known fact that finding a minimum dominating set and consequently the domination number of a general graph is an NP-complete problem‎. ‎In this paper‎, ‎we first model it as a nonlinear binary optimization problem and then extract two closely related semidefinite relaxations‎. ‎For each of these relaxations‎, ‎different rounding algorithm is exp...
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 کاملDominating Set on Bipartite Graphs
Finding a dominating set of minimum cardinality is an NP-hard graph problem, even when the graph is bipartite. In this paper we are interested in solving the problem on graphs having a large independent set. Given a graph G with an independent set of size z, we show that the problem can be solved in time O∗(2n−z), where n is the number of vertices of G. As a consequence, our algorithm is able t...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2008
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2007.03.010