华东师范大学学报(自然科学版) ›› 2008, Vol. 2008 ›› Issue (3): 37-44,1.

• 数学 统计学 • 上一篇    下一篇

2-连通图的单圈子圈

李时银, 白云, 董倩, 任韩   

  1. 华东师范大学 数学系, 上海 200062
  • 收稿日期:2007-05-23 修回日期:2007-10-23 出版日期:2008-05-25 发布日期:2008-05-25
  • 通讯作者: 任韩

Unicyclic subgraphs in 2-connected graphs(Chinese)

LI Shi-yin, BAI Yun, DONG Qian, REN Han   

  1. Department of Mathematics, East China Normal University, Shanghai 20062, China
  • Received:2007-05-23 Revised:2007-10-23 Online:2008-05-25 Published:2008-05-25
  • Contact: REN Han

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摘要： 证明了如下结果:(1) 一个2-连通图的⊙-图是2(p-1)连通的; (2)如果一个2-连通图G有两个单圈支撑子图, 且这两个单圈支撑子图分别含m和n个悬挂点(m<n), 则图G至少有2(p-1)个含k个悬挂点的单圈支撑子图, 这里m≦k≦n, p=|E(G)|-|V(G)|+1.

关键词: 2-连通图, 单圈支撑子图, ⊙-图, 邻⊙-图, 2-连通图, 单圈支撑子图, ⊙-图, 邻⊙-图

Abstract: This paper proved the following results:(1) The ⊙-graph of a 2-connected graph is 2(p-1) connected; (2) if a 2-connected graph G has two unicyclic spanning subgraphs and the number of one-valent vertices of these two subgraphs are respectively m and n (m<n), then for any integer k:m≦k≦n,there exist at least 2(p-1) unicyclic subgraphs of graph G whick have k one-valent vertices. Here, p is the dimension of the cycle space of G.

Key words: 2-connected graph, unicyclic spanning subgraph, ⊙-graph, adjacent ⊙-graph, cut edge, 2-connected graph, unicyclic spanning subgraph, ⊙-graph, adjacent ⊙-graph

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