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圈的扩展与Hamilton圈

发表时间:2014-07-15  浏览量:1552  下载量:435
全部作者: 谢应泰
作者单位: 成都大学信息科学与技术学院
摘 要: 讨论两不相邻的顶点度之和与可扩性的关系,从另一个方向得到关于图的度与扩圈关系的结果。发展可扩概念到“路可扩”与“圈可扩”,并用从一个初始圈逐渐扩展为一个Hamilton圈的方法简洁证明了著名的Fan-定理:G是2-连通图,如果d(u, v)=2!襪ax(d(u), d(v))≥2, 则G有Hamilton圈。
关 键 词: 图论;结合点;可扩圈;Hamilton路;Hamilton圈
Title: Extending cycles and Hamilton cycle
Author: XIE Yingtai
Organization: College of Information Science and Technology, Chengdu University
Abstract: In this paper, the relations between degree sums of two vertices and extending cycles in graphs have been discussed. A similar result is obtained in a new direction. Then, this paper studies the condition for a cycle extending to a cycle including all vertices of a path or an another cycle. By extending a cycle to Hamilton cycle, the following well known Fan-theorem “Let G be a 2-connected graph, if d(u,v)=2!襪ax(d(u),d(v))≥2 then G is Hamiltonian” has been proved simply.
Key words: graph theory; joints; extending cycle; Hamilton path; Hamilton cycle
发表期数: 2014年7月第13期
引用格式: 谢应泰. 圈的扩展与Hamilton圈[J]. 中国科技论文在线精品论文,2014,7(13):1236-1239.
 
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