Rainbow matchings in properly edge colored graphs (Q640415)

Summary: 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 \(\delta \) denote the minimum degree of \(G\). We show that if \(|V (G)| \geq \frac{8\delta}{5} \), then \(G\) has a rainbow matching of size at least \(\lfloor \frac{3\delta}{5} \rfloor \). We also prove that if \(G\) is a properly colored triangle-free graph, then \(G\) has a rainbow matching of size at least \(\lfloor \frac{2\delta }{3}\rfloor \).