Directed Bipartite Graphs Containing Every Possible Pair of Directed Cycles

Let \(D = (V_1, V_2; A)\) be a directed bipartite graph with \(|V_1| = |V_2| = n \geq 2\). Suppose that \(d_D(x) + d_D(y) \geq 3n\) for all \(x \in V_1\) and \(y \in V_2\). Then, with one exception, \(D\) contains two vertex-disjoint directed cycles of lengths \(2s\) and \(2t\), respectively, for any two positive integers \(s\) and \(t\) with \(s+t \leq n\).