| 关于图的3-条件色数 |
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| 引用本文： | 刘婷,孙磊.关于图的3-条件色数[J].数学研究及应用,2014,34(1):43-48. |
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| 作者姓名： | 刘婷 孙磊 |
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| 作者单位： | 山东师范大学数学科学学院, 山东 济南 250014;山东师范大学数学科学学院, 山东 济南 250014 |
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| 基金项目： | 山东省高等学校科技计划项目(Grant No.J10LA11), 山东省自然科学基金(Grant No.ZR2010AQ003). |
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| 摘 要： | For integers k0,r0,a(k,r)-coloring of a graph G is a proper k-coloring of the vertices such that every vertex of degree d is adjacent to vertices with at least min{d,r}diferent colors.The r-hued chromatic number,denoted byχr(G),is the smallest integer k for which a graph G has a(k,r)-coloring.Define a graph G is r-normal,ifχr(G)=χ(G).In this paper,we present two sufcient conditions for a graph to be 3-normal,and the best upper bound of 3-hued chromatic number of a certain families of graphs.
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| 关 键 词： | 着色 上图 顶点 整数 色数 色调 邻接 度数 |
| 收稿时间： | 2012/7/23 0:00:00 |
| 修稿时间： | 2013/2/19 0:00:00 |
On 3-Hued Coloring of Graphs |
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| Ting LIU and Lei SUN.On 3-Hued Coloring of Graphs[J].Journal of Mathematical Research with Applications,2014,34(1):43-48. |
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| Authors: | Ting LIU and Lei SUN |
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| Institution: | School of Mathematical Sciences, Shandong Normal University, Shangdong 250014, P. R. China;School of Mathematical Sciences, Shandong Normal University, Shangdong 250014, P. R. China |
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| Abstract: | For integers $k>0$, $r>0$, a $(k,r)$-coloring of a graph $G$ is a proper $k$-coloring of the vertices such that every vertex of degree $d$ is adjacent to vertices with at least $\min\{d,r\}$ different colors. The $r$-hued chromatic number, denoted by $\chi_r(G)$, is the smallest integer $k$ for which a graph $G$ has a $(k,r)$-coloring. Define a graph $G$ is $r$-normal, if $\chi_r(G)=\chi(G)$. In this paper, we present two sufficient conditions for a graph to be $3$-normal, and the best upper bound of $3$-hued chromatic number of a certain families of graphs. |
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| Keywords: | $r$-hued chromatic number $3$-normal graph triangle |
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