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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ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics