| 平面图的强边染色 |
| |
| 引用本文： | 卜月华,张恒.平面图的强边染色[J].运筹学学报,2022,26(2):111-127. |
| |
| 作者姓名： | 卜月华 张恒 |
| |
| 作者单位： | 1. 浙江师范大学数学与计算机科学学院, 浙江金华 3210042. 浙江师范大学行知学院, 浙江兰溪 321100 |
| |
| 基金项目： | 国家自然科学基金(11771403) |
| |
| 摘 要： | 图$G$的强边染色是在正常边染色的基础上, 要求距离不超过$2$的任意两条边染不同的颜色, 强边染色所用颜色的最小整数称为图$G$的强边色数。本文首先给出极小反例的构型, 然后通过权转移法, 证明了$g(G)\geq5$, $\Delta(G)\geq6$且$5$-圈不相交的平面图的强边色数至多是$4\Delta(G)-1$。
|
| 关 键 词： | 平面图 强边染色 围长 圈 |
| 收稿时间： | 2019-03-05 |
Strong edge-coloring of planar graphs |
| |
| Institution: | 1. College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, Zhejiang, China2. College of Xingzhi, Zhejiang Normal University, Lanxi 321100, Zhejiang, China |
| |
| Abstract: | A strong edge coloring of graph $G$ is on the basis of the proper edge coloring and requiring any two edges at distance at most 2 receive distinct colors, the smallest integer of strong edge coloring called a figure of colors used strong edge chromatic number of $G$. In this paper, the configuration of the minimal counter example is given, and then the power transfer method is used to prove that the strong chromatic index of plane graphs with $g(G)\geq5$, $\Delta(G)\geq6$ and $5$-cycle do not intersect is at most $4\Delta(G)-1$. |
| |
| Keywords: | planar graph strong edge-coloring girth cycle |
|
| 点击此处可从《运筹学学报》浏览原始摘要信息 |
| 点击此处可从《运筹学学报》下载免费的PDF全文 |
|
