| 关于图的点可区别边染色猜想的一点注 |
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| 引用本文： | 王治文,朱恩强,文飞,李敬文.关于图的点可区别边染色猜想的一点注[J].数学的实践与认识,2010,40(2). |
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| 作者姓名： | 王治文 朱恩强 文飞 李敬文 |
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| 作者单位： | 1. 宁夏大学数学计算机学院,宁夏,银川,750021
2. 兰州交通大学应用数学研究所,甘肃,兰州,730070 |
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| 基金项目： | 国家自然科学基金(10771091); 宁夏大学科学研究基金((E)ndzr09-15) |
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| 摘 要： | 图G的一个k-正常边染色f被称为点可区别的是指任意两点的点及其关联边所染色集合不同,所用最少颜色数被称为G的点可区别边色数,张忠辅教授提出一个猜想即对每一个正整数k≥3,总存在一个最大度为△(G)=k≥3的图G,图G一定有一个子图H,使得G的点可区别的边色数不超过子图的.本文证明了对于最大度△≤6时,猜想正确.
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| 关 键 词： | 子图 边染色 图的点可区别边染色 图的点可区别边色数 |
A Note the Conjecture of Vertex-Distinguishing Edge Coloring of Graphs |
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| WANG Zhi-wen,ZHU En-qiang,WEN Fei,LI jing-wen.A Note the Conjecture of Vertex-Distinguishing Edge Coloring of Graphs[J].Mathematics in Practice and Theory,2010,40(2). |
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| Authors: | WANG Zhi-wen ZHU En-qiang WEN Fei LI jing-wen |
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| Institution: | WANG Zhi-wen~1,ZHU En-qiang~2,WEN Fei~2,LI jing-wen~(1,2) (1.School of Mathematics , Computer Science Ningxia University,Yinchuan 750021,China) (2.Instituteof Applied Mathematices,Lanzhou Jiaotong University,Lanzhou 730070,China) |
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| Abstract: | A proper edge coloring of a simple graph G is called vertex distinguishing if for any two distinct vertices u and v in G,the set of colors assigned to the edges incident to u differs from the set of colors incident to v.The minimal number of colors required for a vertex distinguishing edge coloring of G is denoted by x'_(vd)(G).Professor Zhang Zhongfu presented a Conjecture:For k = 3,4,…,there always exists a graph G such that△(G) = k, and there is a subgraph H of G,it usable x'_(vd)(H)>x'_(vd)(G).In this paper,we proved the conjecture is ture for△≤6. |
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| Keywords: | subgraphs edge coloring vertex-distinguishing edge coloring vertex-distinguishing edge chromatic number |
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