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arXiv · 1607.01880

Complete Description of Matching Polytopes with One Linearized Quadratic Term for Bipartite Graphs

Matthias Walter
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Abstract

We consider, for complete bipartite graphs, the convex hulls of characteristic vectors of all matchings, extended by a binary entry indicating whether the matching contains two specific edges. These polytopes are associated to the quadratic matching problems with a single linearized quadratic term. We provide a complete irredundant inequality description, which settles a conjecture by Klein (Ph.D. thesis, TU Dortmund, 2015). In addition, we also derive facetness and separation results for the polytopes. The completeness proof is based on a geometric relationship to a matching polytope of a nonbipartite graph. Using standard techniques, we finally extend the result to capacitated b-matchings.

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Matthias Walter. 2016-07-07. Complete Description of Matching Polytopes with One Linearized Quadratic Term for Bipartite Graphs. https://arxiv.org/abs/1607.01880

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