# Talk:Rainbow matchings in bipartite graphs

From Egres Open

A weaker version of the matroid generalization is mentioned at Talk:List colouring of two matroids. This weaker version is true for matchings by Galvin's bipartite list-edge-colouring theorem.

## Results of Barát and Wanless -- Tamás Király (talk) 13:37, 25 May 2014 (UTC)

A possible strengthening of the conjecture would be to consider *t* matchings of size *k+1* and *k-t* matchings of size *k*. This paper of Barát and Wanless shows that *t* cannot be smaller than [math]\lfloor k/2 \rfloor[/math].