Large rainbow matchings in general graphs

Ron Aharoni; Eli Berger; Maria Chudnovsky; David Howard; Paul Seymour

doi:10.1016/j.ejc.2019.01.012

Large rainbow matchings in general graphs

Ron Aharoni, Eli Berger, Maria Chudnovsky, David Howard, Paul Seymour

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

By a theorem of Drisko, any 2n−1 matchings of size n in a bipartite graph have a rainbow matching of size n. Inspired by results and discussion of Barát, Gyárfás and Sárközy, we conjecture that if n is odd then the same is true also in general graphs, and that if n is even then 2n matchings of size n suffice. We prove that any 3n−2 matchings of size n have a rainbow matching of size n.

Original language	English
Pages (from-to)	222-227
Number of pages	6
Journal	European Journal of Combinatorics
Volume	79
DOIs	https://doi.org/10.1016/j.ejc.2019.01.012
State	Published - Jun 2019

Bibliographical note

Funding Information:
The research of the first author was supported by BSF, Israel Grant No. 2006099, by ISF, Israel Grant No. 2023464, by the Technion's research promotion fund, Israel, and by the Discont Bank chair, Israel..The research of the second author was supported by BSF Grant No. 2006099 and by ISF Grant No. 2023464.The research of the third author was supported by BSF Grant No. 2006099, and NSF grants DMS-1001091 and IIS-1117631..The research of the fourth author was supported by BSF Grant No. 2006099, and by ISF Grant Nos. 779/08, 859/08 and 938/06..The research of the fifth author was supported by ONR grant N00014-14-1-0084 and NSF grant DMS-1265563.. We are grateful to Danny Kotlar and Tung Nguyen for useful remarks.

Publisher Copyright:
© 2019 Elsevier Ltd

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

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10.1016/j.ejc.2019.01.012

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@article{106d3674699a436bb4938fccac3be175,

title = "Large rainbow matchings in general graphs",

abstract = "By a theorem of Drisko, any 2n−1 matchings of size n in a bipartite graph have a rainbow matching of size n. Inspired by results and discussion of Bar{\'a}t, Gy{\'a}rf{\'a}s and S{\'a}rk{\"o}zy, we conjecture that if n is odd then the same is true also in general graphs, and that if n is even then 2n matchings of size n suffice. We prove that any 3n−2 matchings of size n have a rainbow matching of size n.",

author = "Ron Aharoni and Eli Berger and Maria Chudnovsky and David Howard and Paul Seymour",

note = "Funding Information: The research of the first author was supported by BSF, Israel Grant No. 2006099, by ISF, Israel Grant No. 2023464, by the Technion's research promotion fund, Israel, and by the Discont Bank chair, Israel..The research of the second author was supported by BSF Grant No. 2006099 and by ISF Grant No. 2023464.The research of the third author was supported by BSF Grant No. 2006099, and NSF grants DMS-1001091 and IIS-1117631..The research of the fourth author was supported by BSF Grant No. 2006099, and by ISF Grant Nos. 779/08, 859/08 and 938/06..The research of the fifth author was supported by ONR grant N00014-14-1-0084 and NSF grant DMS-1265563.. We are grateful to Danny Kotlar and Tung Nguyen for useful remarks. Publisher Copyright: {\textcopyright} 2019 Elsevier Ltd",

year = "2019",

month = jun,

doi = "10.1016/j.ejc.2019.01.012",

language = "English",

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pages = "222--227",

journal = "European Journal of Combinatorics",

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AU - Aharoni, Ron

AU - Berger, Eli

AU - Chudnovsky, Maria

AU - Howard, David

AU - Seymour, Paul

N1 - Funding Information: The research of the first author was supported by BSF, Israel Grant No. 2006099, by ISF, Israel Grant No. 2023464, by the Technion's research promotion fund, Israel, and by the Discont Bank chair, Israel..The research of the second author was supported by BSF Grant No. 2006099 and by ISF Grant No. 2023464.The research of the third author was supported by BSF Grant No. 2006099, and NSF grants DMS-1001091 and IIS-1117631..The research of the fourth author was supported by BSF Grant No. 2006099, and by ISF Grant Nos. 779/08, 859/08 and 938/06..The research of the fifth author was supported by ONR grant N00014-14-1-0084 and NSF grant DMS-1265563.. We are grateful to Danny Kotlar and Tung Nguyen for useful remarks. Publisher Copyright: © 2019 Elsevier Ltd

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N2 - By a theorem of Drisko, any 2n−1 matchings of size n in a bipartite graph have a rainbow matching of size n. Inspired by results and discussion of Barát, Gyárfás and Sárközy, we conjecture that if n is odd then the same is true also in general graphs, and that if n is even then 2n matchings of size n suffice. We prove that any 3n−2 matchings of size n have a rainbow matching of size n.

AB - By a theorem of Drisko, any 2n−1 matchings of size n in a bipartite graph have a rainbow matching of size n. Inspired by results and discussion of Barát, Gyárfás and Sárközy, we conjecture that if n is odd then the same is true also in general graphs, and that if n is even then 2n matchings of size n suffice. We prove that any 3n−2 matchings of size n have a rainbow matching of size n.

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ER -

Large rainbow matchings in general graphs

Abstract

Bibliographical note

ASJC Scopus subject areas

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