Rainbow matchings in Dirac bipartite graphs

TL;DR

This paper proves the existence of rainbow perfect matchings in certain bipartite graphs with bounded edge colorings and applies these results to find rainbow factors and spanning subgraphs in large minimum degree graphs.

Contribution

It establishes new conditions for rainbow perfect matchings in Dirac bipartite graphs and extends these results to rainbow k-factors and spanning subgraphs.

Findings

Rainbow perfect matchings exist in μn-bounded Dirac bipartite graphs for small μ.

Results on rainbow k-factors in Dirac graphs.

Existence of rainbow spanning subgraphs with bounded degree.

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.