  A rainbow subgraph in an edge-coloured graph is a subgraph such that its
edges have distinct colours. The minimum colour degree of a graph is the
smallest number of distinct colours on the edges incident with a vertex over
all vertices. Kostochka, Pfender, and Yancey showed that every edge-coloured
graph on $n$ vertices with minimum colour degree at least $k$ contains a
rainbow matching of size at least $k$, provided $n\geq (17/4)k^2$. In this
paper, we show that $n\geq 4k-4$ is sufficient for $k \ge 4$.

Combinatorics