图的点可区别的分数边染色数  

Fractional Chromatic Number of Adjacent-Vertex Distinguishing Edge Coloring

作　　者：刘海涛[1,2] 张强 LIU Hai-tao ZHANG Qiang(School of Mathematics, Lanzhou City University, Lanzhou 730070, China School of Management and Economics, Beijing Institute of Technology, Beijing 100081, China)

机构地区：[1]兰州城市学院数学学院,甘肃兰州730070 [2]北京理工大学管理与经济学院,北京100081

出　　处：《数学的实践与认识》2017年第19期245-250,共6页Mathematics in Practice and Theory

基　　金：甘肃省高等学校科研项目(2013A-097);国家自然科学基金(71371030;71561022)

摘　　要：讨论了图的点可区别的边染色数在分数图论的拓展,采用分数图论中超图的a:b-染色方法,证明了邻点可区别的分数边染色数与分数边染色数的等价性,同时进一步推导出经典图论中几类点可区别的边染色数概念如κ-D(β)-点可区别的边染色数、点可区别的边染色数和边染色数也在分数图论的拓展下具有等价性.In this paper, we discuss the relationship between the fractional adjacent-vertex distinguishing edge chromatic number and the fractional edge chromatic number. Based on the a：b-coloring method in the fractional hypergraph, the equivalence of the fractional adjacentvertex distinguishing edge chromatic number and the fractional edge chromatic number are proved, as well as some fractional strong edge chromatic numbers such as the fractional κ-D（β）-vertex distinguishing edge chromatic number, the fractional vertex distinguishing edge chromatic number and the fractional edge chromatic number are all equal.

关 键 词：邻点可区别 边染色数 分数染色 等价性 超图 

分 类 号：O157.5[理学—数学]