Cycle systems in the complete bipartite graph plus a one-factor

Let Kn,n denote the complete bipartite graph with n vertices in each partite set and Kn,n+I denote Kn,n with a one-factor added. It is proved in this paper that there exists an m-cycle system of Kn,n + I if and only if n ≡ 1 (mod 2), m ≡ 0 (mod 2), 4 ≤ m ≤ 2n, and n(n + 1) ≡ 0 (mod m).Published versio