On the independent dominating set polytope

Authors:
A. R. Mahjoub;J. Mailfert
Affiliations:
Laboratoire LIMOS, Université de Clermont II, Aubière Cedex, France;Laboratoire LIMOS, Université de Clermont II, Aubière Cedex, France
Venue:
European Journal of Combinatorics
Year:
2006

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Abstract

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.