On the independent dominating set polytope

Mahjoub, Ali Ridha; Mailfert, Jean

Mahjoub, Ali Ridha; Mailfert, Jean (2006), On the independent dominating set polytope, European Journal of Combinatorics, 27, 4, p. 601-616. http://dx.doi.org/10.1016/j.ejc.2004.07.015

Type

Article accepté pour publication ou publié

Date

2006

Journal name

European Journal of Combinatorics

Volume

Number

Publisher

Elsevier

Pages

601-616

Abstract (EN)

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 for these inequalities. As a consequence, we obtain a polynomial time cutting plane algorithm for the minimum (maximum) independent dominating set problem on a cycle. We also introduce a lifting operation called twin operation, and discuss some polyhedral consequences. In particular, we show that the above results can be extended to a more general class of graphs.

Subjects / Keywords

Polynomial time separation algorithm; Graph; Polytope