A sufficient condition for graphs to be fractional (k, m)-deleted graphs

Let G be a graph, and k a positive integer. Let h : E(G) -> [0, 1] be a function. If Sigma(e epsilon x) h(e) = k holds for each x epsilon V(G), then we call G vertical bar F(h vertical bar) a fractional k-factor of G with indicator function h where F(h) = {e epsilon E(G) : h(e) > 0}. A graph G is called a fractional (k, m)deleted graph if there exists a fractional k-factor G vertical bar F(h)vertical bar of G with indicator function It such that h(e) = 0 for any e epsilon E(H), where H is any subgraph of G with m edges. In this paper, we use a binding number to obtain a sufficient condition for a graph to be a fractional (k, m)deleted graph. This result is best possible in some sense, and it is an extension of Zhou's previous results. (C) 2011 Elsevier Ltd. All rights reserved.