关于3-正则图的平均亏格(英文)  

On the Average Genus of 3-Regular Graphs

作　　者：黄元秋[1,2] 刘彦佩[3,2] 

机构地区：[1]湖南师范大学数学系,长沙湖南410081 [2]中国 [3]北方交通大学数学系,北京100044

出　　处：《数学进展》2002年第1期56-64,共9页Advances in Mathematics（China）

基　　金：This work is supported by the National Natural Science Foundation of China (Grant Number: 19801013).

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．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.

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 

分 类 号：O157.5[理学—数学]