A degree condition of 2-factors in bipartite graphs

Let G=(V1,V2;E) be a bipartite graph with |V1|=|V2|=n, and σ2(G)=min{d(u)+d(v): u,v∈V(G),uv∉E(G)}. In this paper, we show that G has a 2-factor which exactly contains k independent cycles if σ2(G)⩾n+2 for any 1⩽k⩽⌊(n−1)/2⌋, and we also show that the result is sharp.