| 简单平面图中短圈数目的估计 |
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| 引用本文： | 唐保祥,施莉骅,任韩.简单平面图中短圈数目的估计[J].华东师范大学学报(自然科学版),2013,2013(1):11-16. |
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| 作者姓名： | 唐保祥 施莉骅 任韩 |
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| 作者单位： | 1. 天水师范学院数学与统计学院,甘肃,741001
2. 华东师范大学数学系,上海,200241 |
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| 基金项目： | 国家自然科学基金(117114) |
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| 摘 要： | 证明一个n阶简单2-连通平面图G中至多有O(n2)个最短圈(即存在绝对常数c>0使得G中至多有cn2)个最短圈(即存在绝对常数c>0使得G中至多有cn2个最短圈),且该界就n的量级来讲是最好可能的,K_(n-2,2)表明了n2个最短圈),且该界就n的量级来讲是最好可能的,K_(n-2,2)表明了n2是可以达到的量级.
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| 关 键 词： | 短圈 基本圈 Jordan曲线定理 |
| 收稿时间： | 2011-12-01 |
Estimating the number of short cycles in simple planar graphs |
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| TANG Bao-xiang
,
SHI Li-hua
,
REN Han.Estimating the number of short cycles in simple planar graphs[J].Journal of East China Normal University(Natural Science),2013,2013(1):11-16. |
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| Authors: | TANG Bao-xiang SHI Li-hua REN Han |
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| Institution: | 1.School of Mathematics and Statistics Institute,Tianshui Normal University, Gansu 741001,China; 2.Department of Mathematics,East China Normal University,Shanghai 200241,China) |
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| Abstract: | This paper showed that the number of the shortest cycles
in a planar graph of order $n$ is at most $O(n^{2})$ and the bound
is the best possible (subject to the power of $n$) since $K_{n-2,n}$
contains
exactly $\frac{(n-2)(n-3)}{2}$ many 4-cycles. |
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| Keywords: | |
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