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Let G be a graph, and let g, f be two nonnegative integervalued functions defined on V (G) with g(x) ≤ f(x) for each x ∈ V (G). A graph G is called a fractional (g, f, n)-critical graph if after deleting any n vertices of G the remaining graph of G admits a fractional (g, f)factor. In this paper, we obtain a binding number condition for a graph to be a fractional (g, f, n)-critical graph, which is an extension of Zhou and Shen’s previous result (S. Zhou, Q. Shen, On fractional (f, n)-critical graphs, Inform. Process. Lett. 109(2009)811–815). Furthermore, it is shown that the lower bound on the binding number condition is sharp. AMS Mathematics Subject Classification : 05C70, 05C72, 05C35.

BINDING NUMBERS AND FRACTIONAL (g, f, n)-CRITICAL GRAPHS