Let G be a properly colored bipartite graph. A rainbow matching of G is such a matching in which no two edges have the same color. Let G be a properly colored bipartite graph with bipartition (X,Y) and . We show that ...Let G be a properly colored bipartite graph. A rainbow matching of G is such a matching in which no two edges have the same color. Let G be a properly colored bipartite graph with bipartition (X,Y) and . We show that if , then G has a rainbow coloring of size at least .展开更多
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 colored bipartite graph. A rainbow matching of G is such a matching in which no two edges have the same color. Let G be a properly colored bipartite graph with bipartition (X,Y) and . We show that if , then G has a rainbow coloring of size at least .
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.
基金supported partially by NSFC(Nos.11271204,11301371)Central South University of Forestry and Technology Project(No.(104|0292)0292)+2 种基金supported by Tianjin Normal University Project(No.52XB1206)Program for Innovative Research Team in Universities of Tianjin(No.TD13-5078)Science and Technology Development Project of Universities of Tianjin(No.JW1713)
