Many-to-many disjoint paths in faulty hypercubes

This paper considers the problem of many-to-many disjoint paths in the hypercube image with image faulty vertices and image faulty edges, and obtains the following result. For any integer k with image, any two sets S and T of k fault-free vertices in different parts, if image, then there exist k disjoint fault-free image-paths in image which contains at least image vertices. This result is optimal in the worst case.