3-连通图支撑树上的可去边数  

The Number of Removable Edges in a Spanning Tree of a 3-Connected Graph

作　　者：王广富[1] 王燕[2] 

机构地区：[1]保山师范高等专科学校数学系,云南保山678000 [2]烟台大学数学与信息科学学院,山东烟台264005

出　　处：《甘肃科学学报》2007年第3期9-11,共3页Journal of Gansu Sciences

基　　金：国家自然科学基金(10571005)

摘　　要：设e是3-连通图G的一条边,若G-e是某个3-连通图的部分图,则称e是G的可去边.我们对3-连通图G的支撑树上可去边数进行了研究,给出了"阶至少为6且最小度为4(或围长至少为4)的3-连通图G的支撑树上的可去边数至少为2"的简化证明,证明了3-连通3正则图的支撑树上至少有2条可去边.Let e be an edge of a 3-connected graph G. If G-e is a subdivision of a 3-connected graph, then e is called a removable edge of G. In this paper, we study the number of removable edges in a spanning tree of a 3-connected graph and simply verify that ＂Let G be a 3-connected graph with ｜V（G）｜≥/6 and δ（G）≥ 4 （or g（G）≥4）, then the number of removable edges in a spanning tree of G is no less than 2. ＂ and prove that any tree of a 3-connected 3-regular graph has at least two removable edges.

关 键 词：3-连通图 可去边 边点割断片 支撑树 

分 类 号：O157.5[理学—数学]