探索2-边连通图的等价定义  

Probing equivalent definitions of 2-edge connected graphs

作　　者：苏静[1] 马飞[1] 姚兵[1] 

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《华东师范大学学报（自然科学版）》2017年第1期19-25,共7页Journal of East China Normal University(Natural Science)

基　　金：国家自然科学基金(61163054;61163037;61363060)

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.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.

关 键 词：2-边连通图 耳边分解 块 迹 圈 

分 类 号：O157.5[理学—数学]