| 关于3-正则图的平均亏格 |
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| 引用本文： | 黄元秋,刘彦佩. 关于3-正则图的平均亏格[J]. 数学进展, 2002, 31(1): 56-64 |
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| 作者姓名： | 黄元秋 刘彦佩 |
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| 作者单位： | 1. 湖南师范大学数学系,长沙,湖南,410081,中国
2. 北方交通大学数学系,北京,100044,中国 |
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| 基金项目： | This work is supported by the National Natural Science Foundation of China (Grant Number: 19801013). |
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| 摘 要： | 一个图G的2－因子F是一个使得每个点v在F中的度dF(v)=2的G的生成子图。易知F中的每个圈是点不交的。如果F中每个圈的长度为4，我们说G有四边形2－因子F。我们首先在3－正则图上定义了3种扩张运算，然后讨论这些运算对平均亏格的影响。运用扩张运算，我们研究了含有四边形2－因子的3－正则图的平均亏格，得到了3－正则图的平均亏格与最大亏格之间的关系。
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| 关 键 词： | 四边形2－因子 3－正则图 扩张运算 平均亏格 最大亏格 |
On the Average Genus of 3-Regular Graphs |
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| Huang Yuanqiu. On the Average Genus of 3-Regular Graphs[J]. Advances in Mathematics(China), 2002, 31(1): 56-64 |
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| Authors: | Huang Yuanqiu |
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| Abstract: | A 2-factor F, of a graph G, is a spanning subgraph of G such that dF(v) = 2 for any .v V(F). It is obvious that each circuit in F is vertex-disjoint. If the length of every circuIt in F is four, we call that C has a quadrangular 2-factor F. In this paper, we introduce three kinds of extensive operations on a 3-regular graph, and discuss the effect oil the average genus by these extensive operations. Using the extensive operations we then study the average genus of a 3-regular graph containing a quadrangular 2-factor. Finally we give the relationship between the maximum genus .and the average genus of a 3-regular graph. |
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| Keywords: | quadrangular 2-factor 3-regular graphs extensive operation average genus |
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