The dominating set polytope via facility location

Abstract

In this paper we present an extended formulation for the dominating set polytope via facility location. We show that with this formulation we can describe the dominating set polytope for 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 {-1, 0, 1}. This is not the case for the dominating set polytope in the node-variables dimension. It is known from [1] that for any integer , there exists a facet defining inequality having coefficients in {1,...,p} We also show a decomposition theorem by means of 1-sums. Again this decomposition is much simpler with the extended formulation than with the node-variables formulation given in [2]. © 2014 Springer International Publishing.