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应用科学学报 ›› 2003, Vol. 21 ›› Issue (4): 431-434.

• 论文 • 上一篇    

一个充分条件和Hamilton连通图

赵克文1,2, 曾克扬1   

  1. 1 琼州大学数学系 海南 五指山 572200;
    2 海南师范学院数学系 海南 海口 571100
  • 收稿日期:2001-09-20 修回日期:2003-02-11 出版日期:2003-12-10 发布日期:2003-12-10
  • 作者简介:赵克文(1964-),男,海南三亚人,副教授,硕士.
  • 基金资助:
    海南省高校科研资助项目(HjKj200326)

A Sufficient Condition and a Study of Hamilton-Connected Graphs

ZHAO Ke-wen1,2, ZENG Ke-yang1   

  1. 1. Department of Mathematics, Qiongzhou University, Wuzhishan 572200, China;
    2. Department ofMathematics, Hainan Normal University, Haikou 571100, China
  • Received:2001-09-20 Revised:2003-02-11 Online:2003-12-10 Published:2003-12-10

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65

被引次数

4

摘要： 考虑条件:n阶图G的任3个互不相邻的点u、v、w,HN=min{|N(u)∪N(v)|+d(w),|N(v)∪N(w)|+d(u),|N(w)∪N(u)|+d(v)}≥ n.显然,这是一个改进和统一Dirac (W ≥ n/2)和Ore (Ore ≥ n)这两个哈密尔顿图经典条件的条件.此外,HN ≥ n也包含领域并条件NC+W ≥ n.文中研究了HN ≥ n的哈密尔顿图性、哈密尔顿连通图性,得到(I):2连通n阶图G,HN ≥ n则G是哈密尔顿图;(Ⅱ):2连通n阶图G,HN ≥ n则G是哈密尔顿连通图或例外图.

关键词: Hamilton连通图, 新的充分条件, Hamilton图

Abstract: Let G=(V,E) be the simple graph of order n, this shows a new sufficient condition HN ≥ n which imply the three improves and generalizes basic sufficient conditions of Dirac, Ore and neighborhood union. A study of the Hamiltonian, Hamilton connected graphs with HN ≥ n has also been made.

Key words: new sufficient condition, Hamilton-connected graph, Hamiltonian

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