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 5 denote the minimum degree of G. We show that if Iv（G）I 〉 （σ2 ＋ 14σ ＋ 1）/4, then G...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 5 denote the minimum degree of G. We show that if Iv（G）I 〉 （σ2 ＋ 14σ ＋ 1）/4, then G has a rainbow matching of size 6, 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{lXl, IYI} 〉 （σ2 ＋ 4σ - 4）/4, then G has a rainbow matching of size σ.展开更多
文摘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 5 denote the minimum degree of G. We show that if Iv（G）I 〉 （σ2 ＋ 14σ ＋ 1）/4, then G has a rainbow matching of size 6, 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{lXl, IYI} 〉 （σ2 ＋ 4σ - 4）/4, then G has a rainbow matching of size σ.
