Abstract
The simple graph partitioning problem is to partition an edge-weighted graph into mutually disjoint subgraphs, each consisting of no more than b nodes, such that the sum of the weights of all edges in the subgraphs is maximal. In this paper we introduce a large class of facet defining inequalities for the simple graph partitioning polytopes $$\mathcal{P}$$ n (b), b ≥ 3, associated with the complete graph on n nodes. These inequalities are induced by a graph configuration which is built upon trees of cardinality b. We provide a closed-form theorem that states all necessary and sufficient conditions for the facet defining property of the inequalities.
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