2-Factors with a Few Components in Balanced Bipartite Graphs

In this paper, a sufficient condition for a balanced bipartite graph to contain a 2-factor F is given. We show that every balanced bipartite graph of order 2n $\left(n\ge 6\right)$ and $e\left(G\right)>n^2？2n+4$ contains a 2-factor with k components, $2d_1$ -cycle, $？$ , $2d_k$ -cycle, if one of the following is satisfied: (1) $k=2$ , $\delta \left(G\right)\ge 2$ and $d_1？2\ge d_2\ge 2$ ; (2) $k=3$ , $\delta \left(G\right)\ge d_3+2$ and $d_1？2\ge d_2\ge d_3\ge 4$ . In particular, this extends one result of Moon and Moser in 1963 under condition (1).