Rights statement: 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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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - On matroid parity and matching polytopes
AU - Kaparis, Konstantinos
AU - Letchford, Adam
AU - Mourtos, Ioannis
N1 - 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
PY - 2020/9/30
Y1 - 2020/9/30
N2 - 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.
AB - 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.
KW - Matroid parity
KW - Matroid matching
KW - Polyhedral combinatorics
U2 - 10.1016/j.dam.2020.03.049
DO - 10.1016/j.dam.2020.03.049
M3 - Journal article
VL - 284
SP - 322
EP - 331
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
SN - 0166-218X
ER -