A neighborhood condition for graphs to have [a, b]-factors III

Let a, b, k, and m be positive integers such that 1 ≤ a < b and 2 ≤ k ≤ (b + 1 − m)/a. Let G = (V (G), E(G)) be a graph of order |G|. Suppose that |G |> (a + b)(k(a + b − 1) − 1)/b and |NG(x1) ∪ NG(x2) ∪ · · · ∪ NG(xk) | ≥ a|G|/(a + b) for every independent set {x1, x2,..., xk} ⊆ V (G). Then for any subgraph H of G with m edges and δ(G−E(H)) ≥ a, G has an [a, b]-factor F such that E(H) ∩ E(F) = ∅. This result is best possible in some sense and it is an extension of the result of H. Matsuda (Discrete Mathematics 224 (2000) 289–292).