关于直积n_1×n_2×…×n_k的哈密顿圈及哈密顿分解(英文)  

On the Hamiltonian Circuits and Hamiltonian.Decomposition of■×■×…×■

作　　者：黄琼湘[1] 常安[1] 

机构地区：[1]新疆大学数学系,乌鲁木齐,830046,厦门大学数学系,361005

出　　处：《应用数学》1997年第1期46-50,共5页Mathematica Applicata

摘　　要：设n1≤n2≤…≤nk是正整数，D=Cn1×Cn2×…Cnk。是有向圈的直积．在本文中，我们证明了如果ni|nk（1≤i≤k—1），则D含有哈密根图．当n1=n2＝…＝nk时，我们进一步得到D含有[k／2]个弧不交的哈密顿圈．作为副产品，我们推出当是哈密顿有向图时×也是哈密顿有向图．Letn1≤ n2≤… ≤nk be some positire integers. D= Cn1 X C2 X… X Cnk is the cartesian product of directed circuits. In this paper we prove that D has hamiltonian circuits if ni |nk (1≤i≤k 1). When n1 =n2 = … =uk, we confirm that D bas [k/2] arc disjoint hamiltonian circuits, As a byproduct, we deduce that is an hamiltonian digraph if is an hamiltonian digraph.

关 键 词：CAYLEY有向图 哈密顿圈 哈密顿分解 直积 有向圈 

分 类 号：O157.5[理学—数学]