| Issue |
RAIRO-Oper. Res.
Volume 44, Number 1, January-March 2010
|
|
|---|---|---|
| Page(s) | 73 - 83 | |
| DOI | https://doi.org/10.1051/ro/2010005 | |
| Published online | 08 February 2010 | |
Clique-connecting forest and stable set polytopes
LIMOS, Complexe scientifique des Cézeaux,
63177 Aubiere Cedex, France; cornaz@isima.fr
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.
Mathematics Subject Classification: 05C15 / 90C09
Key words: Graph / polytope / separation / facet
© EDP Sciences, ROADEF, SMAI, 2010
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