| 图的f-边覆盖染色 |
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| 引用本文： | 宋慧敏,刘桂真.图的f-边覆盖染色[J].数学学报,2005,48(5):919-928. |
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| 作者姓名： | 宋慧敏 刘桂真 |
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| 作者单位： | [1]山东大学威海分校应用数学系,威海264209 [2]山东大学系统科学与数学学院,济南250100 |
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| 基金项目： | 国家自然科学基金（10471078）;高等学校博士点学科专项基金;山东大学威海分校基金资助项目 |
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| 摘 要： | 设G(V,E)是至少含有一条边的无环图,f厂是定义在V上的整值函数且对任意的v∈V,有1≤f(v)≤d(v).若边染色C使所用的每一种颜色在任一顶点v上至少出现f(v)次,则称该染色C为,f-边覆盖染色.能对图G进行,f-边覆盖k-边染色的最大颜色数k,称为图G的,f-边覆盖色数,记为X'fc(G).本文提供了一个关于X'fc(G)的Vizing型定理,使一些已有重要结论得以推广;研究了一些使X'fc(G)达到该Vizing型定理上界的几类图或函数f,还讨论了f-边覆盖染色的变型,提出了一些可进一步研究的问题.
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| 关 键 词： | 多重图 边染色 f-边覆盖染色 |
| 文章编号： | 0583-1431（2005）05-0919-10 |
| 收稿时间： | 2003-10-20 |
| 修稿时间： | 2003-10-202004-08-16 |
On f-Edge Cover-Coloring of Graphs |
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| Song HuiMin;Liu GuiZhe.On f-Edge Cover-Coloring of Graphs[J].Acta Mathematica Sinica,2005,48(5):919-928. |
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| Authors: | Song HuiMin;Liu GuiZhe |
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| Affiliation: | Hui Min SONG Department of Applied Mathematics, Shandong University at Weihai, Weihai 264209, P. R. China Gui Zhen LIU Department of Mathematics, Shandong University, Jinan 250100, P. R. China |
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| Abstract: | Let G(V, E) be a loop-less graph with at least one edge, and let f be an integer function on V such that 1 ≤ f(v) ≤ d(v) for any v ∈ V. An f-edge cover-coloring is an edge coloring C such that each color appears at each vertex v at least f(v) times. The f-edge cover chromatic index of G, denoted by X'fc(G), is the maximum k such that an f-edge cover k-edge coloring exists. In this paper we provide a Vizing type theorem for X'fc(G) which generalizes a known result. We also investigate graph G or function f such that X'fc(G) attains the upper bound in the Vizing type theorem. A variation |
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| Keywords: | Multiple graph Edge-coloring f-edge cover-coloring |
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