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A rainbow matching in an edge-colored graph is a matching in which no twoedges have the same color. The color degree of a vertex v is the number ofdifferent colors on edges incident to v. Kritschgau [Electron. J. Combin.27(2020)] studied the existence of rainbow matchings in edge-colored graph Gwith average color degree at least 2k, and proved some sufficient conditionsfor 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. Inthis paper, we show that every edge-colored graph G with |V(G)|>=4k-4 andaverage color degree at least 2k-1 contains a rainbow matching of size k. Inaddition, we also prove that every strongly edge-colored graph G with averagedegree at least 2k-1 contains a rainbow matching of size at least k. The boundis sharp for complete graphs.

Large rainbow matchings in edge-colored graphs with given average color degree