Factorizations of the product of cycles

An H-factorization of a graph G is a partition of the edge set of G into spanning subgraphs (or factors) each of whose components are isomorphic to a graph H. Let G be the Cartesian product of the cycles C-1, C-2, ..., C-n with vertical bar C-i vertical bar = 2(ki) >= 4 for each i. El-Zanati and Eynden proved that G has a C-factorization, where C is a cycle of length s, if and only if s = 2(t) with 2 <= t <= k(1) + k(2) + ... + k(n). We extend this result to get factorizations of G into m-regular, m-connected and bipancyclic subgraphs. We prove that for 2 <= m < 2n, the graph G has an H-factorization, where H is an m-regular, m-connected and bipancyclic graph on s vertices, if and only if m divides 2n and s = 2(t) with m <= t <= k(1) + k(2) + ... + k(n) (C) 2018 Kalasalingam University. Publishing Services by Elsevier B.V.