Rainbow matchings in Dirac bipartite graphs

Abstract

We show the existence of rainbow perfect matchings in $\mu n$-bounded edge colourings of Dirac bipartite graphs, for a sufficiently small $\mu >0$. As an application of our results, we obtain several results on the existence of rainbow $k$-factors in Dirac graphs and rainbow spanning subgraphs of bounded maximum degree on graphs with large minimum degree.

20 pages