Complete Description of Matching Polytopes with One Linearized Quadratic Term for Bipartite Graphs
Discrete Mathematics
2019-04-09 v3 Combinatorics
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.
Keywords
Cite
@article{arxiv.1607.01880,
title = {Complete Description of Matching Polytopes with One Linearized Quadratic Term for Bipartite Graphs},
author = {Matthias Walter},
journal= {arXiv preprint arXiv:1607.01880},
year = {2019}
}
Comments
27 pages, 5 figures