边故障超方中距离为偶长的两条顶点不交无故障路

本文得到如下结果：当n≥4时,超立方体Qn中的边故障集F≤n-3,设x1,y1,x 2,y 2是Qn中任意四个顶点,使得x1和y1属于Qn的一部,x2和y2属于Qn的另一部,则在Qn-F中存在两条顶点不交路P1和P2,这里P1连接x1和y1,P2连接x 2和y2,且V（P1）∪V（P2）=V（Qn）,且故障边数n-3是紧的.

Two Vertex-disjoint Fault-free Paths with Even Lengths in a Hypercube with Faulty Edges

In this paper,the following result is obtained.Let Qn be the n - dimensional hypercube,where n ≥4,and F be any subset of edges with F≤ n - 3.Assume that x1,y1,x2,y 2 are any four vertices in Qn such that x1 and y1 belong to a partite set,and x2 and y 2 belong to another partite set in Qn.Then there exist two vertex-disjoint fault-free paths P1 between x1 and y1 and P2 between x2 and y2 such that V（P1） ∪V（P2）= V（Qn）.Moreover,the number n - 3 of faulty edges tolerated is sharp.