A paired k-disjoint path cover (paired k-DPC for short) of a graph is a set of k disjoint paths joining k distinct source-sink pairs that cover all vertices of the graph. Clearly, the paired k-DPC is stronger than Hamiltonian-connectivity. The n-dimensional torus T(k1,k2,…,kn) (including the k-ary n-cube Qnk) is one of the most popular interconnection networks. In this paper, we obtain the following results. (1) Assume even ki≥4 for i=1,2,…,n. Let T=T(k1,k2,…,kn) be a bipartite torus and F be a set of faulty edges with |F|≤2n-3. Given any four vertices s1,t1,s2 and t2, such that each partite set contains two vertices. Then the graph T-F has a paired 2-DPC consisting of s1-t1 path and s2-t2 path. And the upper bound 2n-3 of edge faults tolerated is optimal. The result is a generalization of the result of Park et al. concerning the case of n=2. (2) Assume ki≥3 for i=1,2,…,n, with at most one ki being even. Let T=T(k1,k2,…,kn) be a torus and F be a set of faulty edges with |F|≤2n-4. Then the graph T-F has a paired 2-DPC. And the upper bound 2n-4 of edge faults tolerated is nearly optimal. The result is a generalization of the result of Park concerning the case of n=2. Our brief proofs are based on a technique that is of interest and may find some applications.
