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Clique-connecting forest and stable set polytopes

Published online by Cambridge University Press:  08 February 2010

Denis Cornaz
Denis Cornaz*
Affiliation:
LIMOS, Complexe scientifique des Cézeaux, 63177 Aubiere Cedex, France; cornaz@isima.fr
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Abstract

Let G = (V,E) be a simple undirected graph. A forest F ⊆ E 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.

Keywords

Graphpolytopeseparationfacet
Type
Research Article
Information
RAIRO - Operations Research , Volume 44 , Issue 1 , January 2010 , pp. 73 - 83
Copyright
© EDP Sciences, ROADEF, SMAI, 2010

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