| 不含相邻三角形的平面图的无圈边着色 |
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| 引用本文： | 谢德政,吴燕青. 不含相邻三角形的平面图的无圈边着色[J]. 数学研究及应用, 2012, 32(4): 407-414 |
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| 作者姓名： | 谢德政 吴燕青 |
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| 作者单位： | 重庆大学数学与统计学院, 重庆 401331;重庆大学数学与统计学院, 重庆 401331; 山西师范大学数学与计算机科学学院, 山西 临汾 041000 |
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| 摘 要： | An acyclic edge coloring of a graph G is a proper edge coloring such that there are no bichromatic cycles.The acyclic edge chromatic number of a graph G is the minimum number k such that there exists an acyclic edge coloring using k colors and is denoted by χ’ a(G).In this paper we prove that χ ’ a(G) ≤(G) + 5 for planar graphs G without adjacent triangles.
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| 关 键 词： | acyclic edge coloring acyclic edge chromatic number planar graph. |
| 收稿时间： | 2010-07-07 |
| 修稿时间： | 2011-12-19 |
Acyclic Edge Coloring of Planar Graphs without Adjacent Triangles |
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| Dezheng XIE and Yanqing WU. Acyclic Edge Coloring of Planar Graphs without Adjacent Triangles[J]. Journal of Mathematical Research with Applications, 2012, 32(4): 407-414 |
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| Authors: | Dezheng XIE and Yanqing WU |
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| Affiliation: | College of Mathematics and Statistics, Chongqing University, Chongqing 401331, P. R. China;;College of Mathematics and Statistics, Chongqing University, Chongqing 401331, P. R. China; School of Mathematics and Computer Science, Shanxi Normal University, Shanxi 041000, P. R. China |
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| Abstract: | An acyclic edge coloring of a graph $G$ is a proper edge coloring such that there are no bichromatic cycles. The emph{acyclic edge chromatic number} of a graph $G$ is the minimum number $k$ such that there exists an acyclic edge coloring using $k$ colors and is denoted by $chi'_{a}(G)$. In this paper we prove that $chi'_{a}(G)leq Delta(G)+5$ for planar graphs $G$ without adjacent triangles. |
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| Keywords: | acyclic edge coloring acyclic edge chromatic number planar graph. |
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