Abstract:

The relationship between isolated toughness and existence of fractional (g, f)-factors is considered. It is proved that a graph G has a fractional (g, f)-factor if δ(G) and I(G) are not less than (a+b)²+2(b-a)/4a when a≠b(mod2)or δ(G) and I(G) are not less than (a+b)²+2(b-a)+1/4a  when a≠b(mod2).

Key words: isolated toughness; minimum degree; fractional (g, f)-factor; (g, f)-factor; k-factor