Isolated Toughness and the Existence of f-Factors

Yinghong Ma and Qinglin Yu
School of Management, Shandong Normal University, Shandong 250000, China

Abstract

Let G be a graph with vertex set V(G) and edge set E(G), the isolated toughness of G is defined as I(G)=min{|S|/i(G-S):S V(G), i(G-S) 2} if G is not complete. Otherwise, set I(G)=|V(G)|-1. Let 2 n-1a b be positive integers and ag(x) f(x)b be two nonnegative integral-valued functions defined on V(G). The main results in this paper are to present some sufficient conditions about isolated toughness and minimum degree for graphs to have f-factors and (g,f)-factors (gf). If let f(x)=ab=g(x),, this condition can be improved and the bound is sharp in some sense.