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Existence of rainbow matchings in properly edge-colored graphs
Guanghui WANG, Jianghua ZHANG, Guizhen LIU
Front Math Chin. 2012, 7 (3): 543-550.
https://doi.org/10.1007/s11464-012-0202-9
Let G be a properly edge-colored graph. A rainbow matching of G is a matching in which no two edges have the same color. Let δ denote the minimum degree of G. We show that if |V(G)|>(δ2+14δ+1)/4, then G has a rainbow matching of size δ, which answers a question asked by G. Wang [Electron. J. Combin., 2011, 18: #N162] affirmatively. In addition, we prove that if G is a properly colored bipartite graph with bipartition (X, Y) and max?{|X|,|Y|}>(δ2+4δ-4)/4, then G has a rainbow matching of size δ.
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