Orthogonal double covers of complete bipartite graphs

Let H = {A1, . . . , An, B1, . . . , Bn} be a collection of 2n subgraphs of the complete bipartite graph Kn,n. The collection H is called an orthogonal double cover (ODC) of Kn,n if each edge of Kn,n occurs in exactly two of the graphs in H; E(Ai) ∩ E(Aj) = φ = E(Bi) ∩ E(Bj) for every i, j ∈ {1, . . . , n} with i = j, and for any i, j ∈ {1, . . . , n}, |E(Ai)∩E(Bj)| = 1. If Ai ∼= G ∼= Bi for all i ∈ {1, . . . , n}, then H is called an ODC of Kn,n by G. In this paper, we establish a product construction for ODCs of complete bipartite graphs.