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| 一类平面图的强边染色 | |
| 引用本文： | 孟献青.一类平面图的强边染色[J].山东大学学报(理学版),2015,50(8):10-13. |
| 作者姓名： | 孟献青 |
| 作者单位： | 1. 山西大同大学数学与计算机科学学院, 山西 大同 037009; 2. 山东大学数学学院, 山东 济南 250100 |
| 基金项目： | 山西省青年科技研究基金项目(2013021001-1);山西省高等学校科技研究开发项目(20121015) |
| 摘 要： | 图G的强边染色是指对图G的边进行染色,使得距离不超过2的任意两条边染不同的颜色. 任何一个平面图都可用4Δ+4种颜色进行强边染色. 证明了当平面图没有k-圈(4≤k≤10)且3-圈不相交时(即每个顶点至多关联一个3-圈), 必定存在一个3Δ+1种颜色的强边染色. |
| 关 键 词： | 平面图 强边染色 强边色数 圈 |
| 收稿时间： | 2015-04-17 |
Strong edge coloring of a class of planar graphs |
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| MENG Xian-qing.Strong edge coloring of a class of planar graphs[J].Journal of Shandong University,2015,50(8):10-13. | |
| Authors: | MENG Xian-qing |
| Institution: | 1. School of Mathematics and Computer Sciences, Shanxi Datong University, Datong 037009, Shanxi, China; 2. School of Mathematics, Shandong University, Jinan 250100, Shandong, China |
| Abstract: | A strong edge coloring of a graph G is an assignment of colors to the edges of the graph such that any two edges at distance at most 2 receive distinct colors. It is known that every planar graph has a strong edge-coloring with at most 4Δ+4 colors. It is proved that planar graph G has a strong edge-coloring with at most 3Δ+1 colors if G has no k-cycles with 4≤k≤10 and no intersecting 3-cycles (that is, every vertex is incident with at most one cycle of length 3). |
| Keywords: | planar cycle srtong chromaic index strong edge coloring |
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