Factorizations of the product of cycles. Issue 3 (1st December 2019) - Borse, Y.M.; Sonawane, A.V.; Shaikh, S.R.
Abstract: 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 | C i | = 2 k i ≥ 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 < 2 n, 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 2 n and s = 2 t with m ≤ t ≤ k 1 + k 2 + ⋯ + k n .