Partition of a bipartite Hamiltonian graph into two cycles (Q1072572)

The author proves that any bipartite graph with bipartition \((A,B)\), \(| A| =| B| =n\), such that for every \(u\in A\), \(v\in B\), \(\deg (u)+\deg (v)\geq n+2\), contains two independent cycles of lengths \(2n_1\) and \(2n_2\), whenever \(n_1,n_2\geq 2\) and \(n_1+n_2=n\).