边故障k元n立方体的超级哈密顿交织性

k元n立方体（记为Qkn ）是优于超立方体的可进行高效信息传输的互连网络之一。Qkn是一个二部图当且仅当k为偶数。令GV0,V1]是一个二部图，若（1）任意一对分别在不同部的顶点之间存在一条哈密顿路，且（2）对于任意一点v ∈ Vi ，其中i∈{0,1}，V1-i中任意一对顶点可以被GV0,V1]-v中的一条哈密顿路相连，则图GV0,V1]被称为是超级哈密顿交织的。因为网络中的元件发生故障是不可避免的，所以研究网络的容错性就尤为重要。针对含有边故障的Qkn ，其中k≥4是偶数且n≥2，证明了当其故障边数至多为2n-3时，该故障Qkn是超级哈密顿交织图，且故障边数目的上界2n-3是最优的。

Hyper hamiltonian laceability of k-ary n-cubes with edge faults

The k-aryn-cube, denoted by Qkn , as one of the most efficient interconnection networks for information transportation, has been shown as an alternative to the hypercube. A Qkn is bipartite if and only if k is even. A bipartite graph GV0,V1] is called hyper hamiltonian laceable if（1）it has a hamiltonian path between any pair of vertices in different parts, and（2）for any vertex v∈ Vi , there is a hamiltonian path of GV0,V1]-v between any two vertices in V1-i , where i∈{0,1}. Since edge faults may occur after a network is activated, it is important to solve problems in faulty networks. This paper addresses the faulty Qkn with even k≥4 and n≥2 , and proves that the Qkn with at most 2n-3 faulty edges is hyper hamiltonian laceable. This result is optimal to the number of edge faults tolerated.