BINDING NUMBERS AND F-FACTORS OF GRAPHS

Let G be a connected graph of order n, a and b be integers such that 1 ≤ a ≤ b and 2 ≤ b, and f: V(G) → {a, a + 1, ..., b} be a function such that Σ(f(x); x ∈ V(G)) ≡ 0 (mod 2). We prove the following two results: (i) If the binding number of G is greater than (a + b -1)(n-1) (an-(a + b) + 3) and n ≥ (a + b)2 a, then G has an f-factor; (ii) If the minimum degree of G is greater than (bn - 2) (a + b), and n ≥ (a + b)2 a, then G has an f-factor. © 1992.