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■×■×…×■

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.