On matroid parity and matching polytopes

Kaparis, Konstantinos and Letchford, Adam and Mourtos, Ioannis (2020) On matroid parity and matching polytopes. Discrete Applied Mathematics, 284. pp. 322-331. ISSN 0166-218X

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The matroid parity (MP) problem is a powerful (and NP-hard) extension of the matching problem. Whereas matching polytopes are well understood, little is known about MP polytopes. We prove that, when the matroid is laminar, the MP polytope is affinely congruent to a perfect b-matching polytope. From this we deduce that, even when the matroid is not laminar, every Chvátal-Gomory cut for the MP polytope can be derived as a {0,1/2}-cut from a laminar family of rank constraints. We also prove a negative result concerned with the integrality gap of two linear relaxations of the MP problem.

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Journal Article
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Discrete Applied Mathematics
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This is the author’s version of a work that was accepted for publication in Discrete Applied Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Discrete Applied Mathematics, 284, 2020 DOI: 10.1016/j.dam.2020.03.049
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Deposited On:
27 Mar 2020 14:00
Last Modified:
22 Nov 2022 08:54