  A rainbow matching in an edge-colored graph is a matching in which no two
edges have the same color. The color degree of a vertex v is the number of
different colors on edges incident to v. Kritschgau [Electron. J. Combin.
27(2020)] studied the existence of rainbow matchings in edge-colored graph G
with average color degree at least 2k, and proved some sufficient conditions
for a rainbow marching of size k in G. The sufficient conditions include that
|V(G)|>=12k^2+4k, or G is a properly edge-colored graph with |V(G)|>=8k. In
this paper, we show that every edge-colored graph G with |V(G)|>=4k-4 and
average color degree at least 2k-1 contains a rainbow matching of size k. In
addition, we also prove that every strongly edge-colored graph G with average
degree at least 2k-1 contains a rainbow matching of size at least k. The bound
is sharp for complete graphs.
