华东师范大学学报(自然科学版)

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探索 2-边连通图的等价定义

苏静; 马飞; 姚兵;   

  1. 西北师范大学 数学与统计学院, 兰州 730070
  • 收稿日期:2015-12-29 出版日期:2017-01-25 发布日期:2017-01-13
  • 通讯作者: 姚 兵, 男, 教授, 研究方向为图着色与标号以及复杂网络. E-mail: yybb918@163.com.
  • 基金资助:

    国家自然科学基金 (61163054, 61163037, 61363060)

Probing equivalent definitions of 2-edge connected graphs

SU Jing, MA Fei, YAO Bing   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
  • Received:2015-12-29 Online:2017-01-25 Published:2017-01-13

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摘要：

k-边连通图在网络研究和图论研究中有着极其重要的地位. 图论中有关 2- 边连通图的命题很多, 它们刻画了 2- 边连通的本质. 本文给出17种关于2-边连通图的等价性命题, 力图从不同角度深入理解、挖掘 2-边连通图的本征, 并从本文定义的 2 种新运算出发, 提出了新的有关 2-边连通图的命题, 并给出这些命题相互间的等价性证明.

关键词: 2-边连通图, 耳边分解, 块, 迹, 圈

Abstract:

As known, k-edge connected graphs play an important role in the research of networks and graph theory. There are many propositions of 2-edge connected graphs nowadays, which depict the essences of 2-edge connected graphs. We present 17 equivalent propositions of 2-edge connected graphs and dig more properties of 2-edge connected graphs from different aspects of 2-edge connected graphs. Furthermore, two equivalent propositions of 2-edge connected graphs by two new operations are proposed, and then we provide the equivalent proofs between the propositions we have collected and discovered.

Key words: 2-edge connected graph, ear edge decomposition, block, trail, cycle