Decomposition of the Product of Cycles Based on Degree Partition

The Cartesian product of n cycles is a 2n-regular, 2n-connected and bi- pancyclic graph. Let G be the Cartesian product of n even cycles and let 2n = n₁+ n₂+ ・ ・ ・ + n_k with k ≥ 2 and n_i ≥ 2 for each i. We prove that if k = 2, then G can be decomposed into two spanning subgraphs G₁ and G₂ such that each G_i is n_i-regular, n_i-connected, and bipancyclic or nearly bipancyclic. For k > 2, we establish that if all n_i in the partition of 2n are even, then G can be decomposed into k spanning subgraphs G₁, G₂, . . ., G_k such that each G_i is n_i-regular and n_i-connected. These results are analogous to the corresponding results for hypercubes.