| 3连通图的可去边的分布 |
| |
| 引用本文： | 欧见平,苏健基.3连通图的可去边的分布[J].广西师范大学学报(自然科学版),2001,19(1):25-29. |
| |
| 作者姓名： | 欧见平 苏健基 |
| |
| 作者单位： | 广西师范大学数学系，广西 桂林 541004 |
| |
| 基金项目： | 国家自然科学基金资助课题(19561001) |
| |
| 摘 要： | e是3连通图G的一条边，如果G-e是某个3连通图的剖分，则称e是G的可去边。研究了3连通图的去边的分布规律，得到：（1）是阶至少为6的3连通图G中的一个圈，如果C上不存在3个连续的3度点，那么C上至少有两条可去边。（2）设T是阶至少为5的连通图G的一棵生成树，如果G中至多存在一个极大半轮，那么T上至少有一条可去边。由此可得：阶至少为5的3连通3正则图的生成树上至少有一条可去边。
|
| 关 键 词： | 3连通图 可去边 圈 生成树 分布规律 简单无向有限图 极大半轮 |
| 文章编号： | 1001-6600(2001)01-0025-05 |
| 修稿时间： | 2000年10月8日 |
DISTRIBUTION OF REMOVABLE EDGES IN 3-CONNECTED GRAPHS |
| |
| OU Jian-ping.DISTRIBUTION OF REMOVABLE EDGES IN 3-CONNECTED GRAPHS[J].Journal of Guangxi Normal University(Natural Science Edition),2001,19(1):25-29. |
| |
| Authors: | OU Jian-ping |
| |
| Abstract: | An edge e of a 3-connected graph G is said to be removable if G-eis the subdivition of a 3-connected graph.The distribu tion of removable edges in 3-connected graphs is discussed in the paper.The following results are obtained:(1) Let C be a cycle in 3-connected graph G with υ(G)≥6.If this cycle contains no three consecutive vertices wit h degree three,then there are at least two removable edges in it.(2) Let T b e a spanning tree of G with υ(G)≥5.If G contains at most one maxim al semiwheel,then T has at least one removable edge,and thus there is at lea st one removable edge in the spanning tree of 3-connected cubic graphs with ord er at least five. |
| |
| Keywords: | |
| 本文献已被 维普 万方数据 等数据库收录！ |
