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b-Tree Facets for the Simple Graph Partitioning Polytope

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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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  1. Deparment of Management Science and Logistics, The Aarhus School of Business, Fuglesangs Allé 4, Aarhus V, DK-8210, Denmark

    Michael M. Sørensen

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  1. Michael M. Sørensen
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Sørensen, M.M. b-Tree Facets for the Simple Graph Partitioning Polytope. Journal of Combinatorial Optimization 8, 151–170 (2004). https://doi.org/10.1023/B:JOCO.0000031417.96218.26

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  • DOI: https://doi.org/10.1023/B:JOCO.0000031417.96218.26

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