Jeroen H. G. C. Rutten

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The clique partitioning problem (CPP) can be formulated as follows: Given is a complete graph G = (V, E), with edge weights wij ∈ R for all {i, j} ∈ E. A subset A ⊆ E is called a clique partition if there is a partition of V into nonempty, disjoint sets V1, . . . , Vk , such that each Vp (p = 1, . . . ,k) induces a clique (i.e., a complete subgraph), and A(More)
In this paper we prove two lifting theorems for the clique partitioning problem. Each of these theorems implies that if a valid inequality satis es certain conditions, then it de nes a facet of the clique partitioning polytope. In particular if a valid inequality de nes a facet of the polytope corresponding to the graph Km, i.e. the complete graph on m(More)
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