Cycles in 2-factors of balanced bipartite graphs (Q1972322)

Let \(G\) be a balanced bipartite graph of order \(2n\) \((n\geq 2)\) such that \(\deg u+\deg v\geq n+1\) for each pair of non-adjacent vertices from different partite sets. \textit{J. W. Moon} and \textit{L. Moser} [Isr. J. Math. 1, 163-165 (1963; Zbl 0119.38806)] showed that such a graph \(G\) has a spanning cycle. The authors of the present paper show that if \(k\) is a positive integer such that \(n\geq \max\{51,k^2/2+ 1\}\), then such a graph \(G\) also has a 2-factor with exactly \(k\) cycles.