期刊论文

中文

应用数学学报

0254-3079

2015

38

5

796-805

湖北省教育厅科学技术研究项目B2015021；

本校为其他机构

本文证明了任何满足|N(X)|>(n+|X|+ 1)/3,X?Vi的2n阶2-连通平衡二部图G= (V1,V2,E)均为哈密尔顿图.该定理可视为Woodall关于一般图哈密尔顿性的相关定理“任何满足|N(X)|≥(n+|X|- 1)/3,X?V且最小度δ(G)≥(n+2)/3的n阶2-连通图均为哈密尔顿图”的二部图形式.

We investigate a sufficient condition for hamilton cycle occurring in balanced bipartite graphs with the neighborhood of vertex set.In this paper,we apply the structure of D_3-cycle and Bipartite Hopping Lemma to show that any 2-connected balanced bipartite graph on 2n vertices is hamiltonian if it satisfies ｜N（X）｜ （n ＋ ｜X｜ ＋1）/3 for any XV_i.This theorem is the bipartite graph form of the conclusion that any 2-connected graph on n vertices satisfying ｜N（X）｜ （n ＋ ｜X｜-1）/3 for anyΦ ≠X V（G） and the minimum degree δ（G） ≥（n ＋ 2）/3 is...