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.
Bibliographical noteFunding 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.
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ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics