Cycle systems in the complete bipartite graph minus a one-factor Original Research Article

Let Kn,n−I denote the complete bipartite graph with n vertices in each part from which a 1-factor I has been removed. An m-cycle system of Kn,n−I is a collection of m-cycles whose edges partition Kn,n−I. Necessary conditions for the existence of such an m-cycle system are that m⩾4 is even, n⩾3 is odd, m⩽2n, and m | n(n−1). In this paper, we show these necessary conditions are sufficient except possibly in the case that m≡0 (mod 4) with n