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    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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On matroid parity and matching polytopes

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On matroid parity and matching polytopes. / Kaparis, Konstantinos; Letchford, Adam; Mourtos, Ioannis .

In: Discrete Applied Mathematics, Vol. 284, 30.09.2020, p. 322-331.

Research output: Contribution to journalJournal articlepeer-review

Harvard

Kaparis, K, Letchford, A & Mourtos, I 2020, 'On matroid parity and matching polytopes', Discrete Applied Mathematics, vol. 284, pp. 322-331. https://doi.org/10.1016/j.dam.2020.03.049

APA

Vancouver

Kaparis K, Letchford A, Mourtos I. On matroid parity and matching polytopes. Discrete Applied Mathematics. 2020 Sep 30;284:322-331. https://doi.org/10.1016/j.dam.2020.03.049

Author

Kaparis, Konstantinos ; Letchford, Adam ; Mourtos, Ioannis . / On matroid parity and matching polytopes. In: Discrete Applied Mathematics. 2020 ; Vol. 284. pp. 322-331.

Bibtex

@article{fdac537b28754403bcad263716f1f368,
title = "On matroid parity and matching polytopes",
abstract = "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 Chv{\'a}tal-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.",
keywords = "Matroid parity, Matroid matching, Polyhedral combinatorics",
author = "Konstantinos Kaparis and Adam Letchford and Ioannis Mourtos",
note = "This is the author{\textquoteright}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",
year = "2020",
month = sep,
day = "30",
doi = "10.1016/j.dam.2020.03.049",
language = "English",
volume = "284",
pages = "322--331",
journal = "Discrete Applied Mathematics",
issn = "0166-218X",
publisher = "Elsevier",

}

RIS

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 -