Many-to-many disjoint paths in faulty hypercubes

This paper considers the problem of many-to-many disjoint paths in the hypercube QnQn with fvfv faulty vertices and fefe faulty edges, and obtains the following result. For any integer k   with 1⩽k⩽n-11⩽k⩽n-1, any two sets S and T of k   fault-free vertices in different parts, if fv+fe⩽n-k-1fv+fe⩽n-k-1, then there exist k   disjoint fault-free (S,T)(S,T)-paths in QnQn which contains at least 2n-2fv2n-2fv vertices. This result is optimal in the worst case.