在超立方体Q_n中通过给定三条边的所有圈  

Cycles Passing through Prescribed Three Edges in a Hypercube

作　　者：姚晓盼[1] 

机构地区：[1]漳州师范学院数学与信息科学系,福建漳州363000

出　　处：《漳州师范学院学报（自然科学版）》2008年第2期28-31,共4页Journal of ZhangZhou Teachers College（Natural Science)

基　　金：国家自然科学基金资助项目(10671191)

摘　　要：本文研究了在超立方体Qn中通过给定三条边的所有圈的问题.证明了:设E0E(Qn)且|E0|=3≤n.由E0导出的子图是线性森林,则在Qn中E0的所有边包含在长为l的偶圈中,其中l是满足2n+2≤l≤2n的每个偶数.并且下界2n+2是最优的.In this paper, we consider the problem of cycles passing through prescribed three edges in an n-dimensional hypercube Qn. Let E0 belong to E（Qn） and ｜ E0 ｜= 3 ≤ n. If the subgraph induced by E0 is a linear forest （pairwise dispoint paths）, then in the graph Qn three edges of E0 lie on a cycle of every even length l with 2n ＋ 2 ≤ l ≤ 2^n. And the lower bound 2n ＋ 2 is optimal.

关 键 词：超立方体 圈 哈密尔顿圈 嵌入 互连网络 

分 类 号：O157.5[理学—数学]