Sufficient Conditions for a Graph to Have All [a, b]-Factors and (a, b)-Parity Factors

Let G be a graph with vertex set V and let b > a be two positive integers. We say that G has all [a, b]-factors if G has an h-factor for every h : V -> N such that a <= h(v) <= b for every v is an element of V and Sigma(v is an element of V) h(v) 0 (mod 2). A spanning subgraph F of G is called an (a, b)-parity factor, if d(F)(v) a b (mod 2) and a <= d(F) (v) <= b for all v is an element of V. In this paper, we have developed sufficient conditions for the existence of all [a, b]-factors and (a, b)-parity factors of G in terms of the independence number and connectivity of G. This work extended an earlier result of Nishimura (J Graph Theory 13: 63-69, 1989). Furthermore, we show that these results are best possible in some cases.