Existence of rainbow matchings in properly edge-colored graphs

作     者：Guanghui WANG Jianghua ZHANG Guizhen LIU 

作者机构：School of MathematicsShandong UniversityJinan 250100China School of ManagementShandong UniversityJinan 250100China 

出 版 物：《Frontiers of Mathematics in China》 (中国高等学校学术文摘·数学（英文）)

年 卷 期：2012年第7卷第3期

页      面：543-550页

核心收录：

学科分类：1304[艺术学-美术学] 13[艺术学] 08[工学] 080203[工学-机械设计及理论] 0804[工学-仪器科学与技术] 0802[工学-机械工程] 

基　　金：国家自然科学基金 国家教育部高等学校博士学科点专项科研基金 Scientific Research Foundation for the Returned Overseas Chinese Scholars 

主　　题：Rainbow matching properly edge-colored graph 

摘      要：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.