English

运筹学学报 >

2018 , Vol. 22 >Issue 4: 148 - 152

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2018.04.015

运筹学

联图的圈基

展开
  • 1. 中国人民大学数学学院, 北京 100872; 2. 北京第二外国语学院通识教育学院, 北京 100024

收稿日期: 2017-11-01

  网络出版日期: 2018-12-15

基金资助

国家自然科学基金(No. 11401576)

收起

The basis number of join graphs

Expand
  • 1. School of Mathematics, Renmin University of China, Beijing 100872, China; 2. School of General Education, Beijing International Studies University, Beijing 100024, China

Received date: 2017-11-01

  Online published: 2018-12-15

Fold

摘要

MacLane于1937年给出了圈基方面的重要定理: 图G是平面图, 当且仅当图G有2-重基. 连通图G_1和G_2的联图G_1\vee G_2指的是在它们的不交并G_1\bigcup G_2上添加边集(u,v)|u\in V(G_1), v\in V(G_2). 对G_1和G_2的联图G_1\vee G_2的圈基重数进行了研究, 得到了一个上界, 改进了Zare的结果. 并在此基础之上, 进一步得到特殊联图C_m\vee C_n的圈基重数的一个上界.

关键词： 联图; 圈空间; 基

本文引用格式

吕雪征, 魏二玲, 宋宏业 . 联图的圈基[J]. 运筹学学报, 2018 , 22(4) : 148 -152 . DOI: 10.15960/j.cnki.issn.1007-6093.2018.04.015

Abstract

In 1937 MacLane gave the important theory on cycle basis: gaph G is planar if and only if G  has a 2-basis. The join G = G_1\vee G_2 of graphs G_1 and G_2 is obtained from  G_1\bigcup G_2 by adding all the edges in {(u,v)|u\in V(G_1), v\in V(G_2)}. In this paper we investigate the  basis number of G = G_1\vee G_2 and obtain an upper bound which improves the bound given by Zare. Based on this, a better bound of C_m \vee C_n is derived too.

Key words： join of graph; cycle space; basis

Options
文章导航

/

〈 〉