A DEGREE CONDITION FOR GRAPHS TO HAVE CONNECTED (g,f)-FACTORS
Sanming Zhou, H Liu, Ying Xu · 2009
Abstract. Let G be a graph of order n, a and b be integers with 1 ≤ a < b and b ≥ 3, g(x) and f(x) be two integer-valued functions defined on V (G) such that a ≤ g(x) < f(x) ≤ b, for each x ∈ V (G) and f(V (G))−V (G) even. We prove that G has a connected (g, f)-factor if the minimum degree δ(G) satisfies δ(G) ≥ (b−1)n a+b−1 and n ≥