Many-to-many disjoint paths in faulty hypercubes

This paper considers the problem of many-to-many disjoint paths in the hypercube Q n with f v faulty vertices and f e faulty edges, and obtains the following result. For any integer k with 1 ≤ k ≤ n - 1 , any two sets S and T of k fault-free vertices in different parts, if f v + f e ≤ n - k - 1 , then there exist k disjoint fault-free ( S , T ) -paths in Q n which contains at least 2 n - 2 f v vertices. This result is optimal in the worst case.