Abstract
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 distinct colors on edges incident to v. Kritschgau [Electron. J. Combin. 27(3), 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 $$|V(G)|\ge 12k^2+4k$$ , or G is a properly edge-colored graph with $$|V(G)|\ge 8k$$ . In this paper, we show that every edge-colored graph G with $$|V(G)|\ge 4k-4$$ 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.
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