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Title: On matroid parity and matching polytopes
Authors: Kaparis, Konstantinos
Letchford, Adam N.
Mourtos, Ioannis
Type: Article
Subjects: FRASCATI::Natural sciences::Computer and information sciences
Keywords: Matroid parity
Matroid matching
Polyhedral combinatorics
Issue Date: 30-Sep-2020
Publisher: Elsevier
Source: Discrete Applied Mathematics
Volume: 284
First Page: 322
Last Page: 331
Abstract: The matroid parity (MP) problem is a powerful (and -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 -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 -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.
ISSN: 0166-218X
Other Identifiers: 10.1016/j.dam.2020.03.049
Appears in Collections:Department of Business Administration

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