On the independent dominating set polytope
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
TypeArticle accepté pour publication ou publié
Journal nameEuropean Journal of Combinatorics
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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 / KeywordsPolynomial time separation algorithm; Graph; Polytope
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Mailfert, Jean; Mahjoub, Ali Ridha; Didi Biha, Mohamed; Ibrahima, Diarrassouba; Bendali, Fatiha (2010) Article accepté pour publication ou publié