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

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.

DOI : 10.1051/ro/2010005
Classification : 05C15, 90C09
Mots clés : graph, polytope, separation, facet 
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     author = {Cornaz, Denis},
     title = {Clique-connecting forest and stable set polytopes},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {73--83},
     publisher = {EDP-Sciences},
     volume = {44},
     number = {1},
     year = {2010},
     doi = {10.1051/ro/2010005},
     mrnumber = {2642917},
     zbl = {1221.05132},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ro/2010005/}
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Cornaz, Denis. Clique-connecting forest and stable set polytopes. RAIRO - Operations Research - Recherche Opérationnelle, Tome 44 (2010) no. 1, pp. 73-83. doi : 10.1051/ro/2010005. http://www.numdam.org/articles/10.1051/ro/2010005/

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