2-Factors of bipartite graphs with asymmetric minimum degrees

Let G and H be balanced U, V-bigraphs on 2n vertices with δ (H) ≤ 2. Let κ be the number of components of H, δU := min{deg _G(υ): υ ∈ U} and δv := min{deg _G(υ): υ G V}. We prove that if n is sufficiently large and δU +δV ≥ n+κ, then G contains H. This answers a question of Amar in the case that n is large. We also show that G contains H even when δ_U + δ_V ≥ n + 2 as long as n is sufficiently large in terms of κ and δ(G) ≥ n/200κ + 1.