| 关于图的星色数的一点注记 |
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| 引用本文： | 伏红勇,谢德政.关于图的星色数的一点注记[J].数学研究及应用,2010,30(5):841-844. |
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| 作者姓名： | 伏红勇 谢德政 |
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| 作者单位： | 重庆大学数学与统计学院, 重庆 401331; 重庆大学经济与工商管理学院, 重庆 400044;重庆大学数学与统计学院, 重庆 401331 |
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| 基金项目： | 重庆市科委自然科学基金计划资助项目(Grant No.2007BB2123)． |
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| 摘 要： | A star coloring of an undirected graph G is a proper coloring of G such that no path of length 3 in G is bicolored.The star chromatic number of an undirected graph G,denoted by χs(G),is the smallest integer k for which G admits a star coloring with k colors.In this paper,we show that if G is a graph with maximum degree △,then χs(G) ≤ 7△3/2],which gets better bound than those of Fertin,Raspaud and Reed.
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| 关 键 词： | star coloring star chromatic number proper coloring. |
| 收稿时间： | 2008/10/25 0:00:00 |
| 修稿时间： | 2009/5/16 0:00:00 |
A Note on Star Chromatic Number of Graphs |
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| Hong Yong FU and De Zheng XIE.A Note on Star Chromatic Number of Graphs[J].Journal of Mathematical Research with Applications,2010,30(5):841-844. |
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| Authors: | Hong Yong FU and De Zheng XIE |
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| Institution: | 1. College of Mathematics and Statistics,Chongqing University,Chongqing 401331,P.R.China;College of Economics and Business Administration,Chongqing University,Chongqing 400044,P.R.China
2. College of Mathematics and Statistics,Chongqing University,Chongqing 401331,P.R.China |
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| Abstract: | A star coloring of an undirected graph $G$ is a proper coloring of $G$ such that no path of length $3$ in $G$ is bicolored. The star chromatic number of an undirected graph $G$, denoted by $\chi_{s}(G)$, is the smallest integer $k$ for which $G$ admits a star coloring with $k$ colors. In this paper, we show that if $G$ is a graph with maximum degree $\Delta$, then $\chi_{s}(G)\leq\lceil7\Delta^{\frac{3}{2}}\rceil$, which gets better bound than those of Fertin, Raspaud and Reed. |
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| Keywords: | star coloring star chromatic number proper coloring |
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