Clique-connecting forest and stable set polytopes
RAIRO - Operations Research - Recherche Opérationnelle, Volume 44 (2010) no. 1, pp. 73-83.

Let G = (V,E) be a simple undirected graph. A forest FE of G is said to be clique-connecting if each tree of F spans a clique of G. This paper adresses the clique-connecting forest polytope. First we give a formulation and a polynomial time separation algorithm. Then we show that the nontrivial nondegenerate facets of the stable set polytope are facets of the clique-connecting polytope. Finally we introduce a family of rank inequalities which are facets, and which generalize the clique inequalities.

DOI: 10.1051/ro/2010005
Classification: 05C15, 90C09
Keywords: graph, polytope, separation, facet
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Cornaz, Denis. Clique-connecting forest and stable set polytopes. RAIRO - Operations Research - Recherche Opérationnelle, Volume 44 (2010) no. 1, pp. 73-83. doi : 10.1051/ro/2010005. http://archive.numdam.org/articles/10.1051/ro/2010005/

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