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Let be a simple undirected graph.
A forest ⊆ of is said to be if each tree of spans a clique of .
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.
A co-biclique of a simple undirected graph is the edge-set of two disjoint complete subgraphs of .
(A co-biclique is the complement of a biclique.)
A subset is an independent of if there is a co-biclique such that , otherwise is a dependent of . This paper describes the minimal dependents of . (A minimal dependent is a dependent such that any proper subset of is an independent.)
It is showed that a minimum-cost dependent set of can be determined in polynomial time for any nonnegative cost...
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