Large rainbow matchings in general graphs. (June 2019) - Aharoni, Ron; Berger, Eli; Chudnovsky, Maria; Howard, David; Seymour, Paul
Abstract: By a theorem of Drisko, any 2 n − 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 2 n matchings of size n suffice. We prove that any 3 n − 2 matchings of size n have a rainbow matching of size n .