A characterization of graphs having all (g,f)-factors

Let G be a graph with vertex set V and let g. f: V --> Z(+). We say that G has all (g, f)-factors if G has an h-factor for every h: V --> Z(+) such that g(upsilon) less than or equal to h(upsilon) less than or equal to f(upsilon) for every upsilon is an element of V and at least one such h exists. In this nets, we derive from Tutte's f-factor theorem a similar characterization for the properly of having all (g, f)-factors. An analogous result for parity-factors is presented also. (C) 1998 Academic Press.