Embeddings of cycles, meshes and tori in faulty k-ary n-cubes

We investigate the existence of cycles, meshes and tori in a k-ary n-cube Q_n^k in which a limited number of nodes and links are faulty. Our main result is that in a k-ary n-cube Q_n^k in which there are v faulty nodes λfaulty links where v+λ⩽n, there is a cycle of length at least kⁿ-vw, where w=1 if k is odd and w=2 if k is even (throughout k⩾3 and n⩾2). We extend this result so as to prove the existence of large meshes and tori in such a faulty k-ary n-cube