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BINDING NUMBERS AND FRACTIONAL (g, f, n)-CRITICAL GRAPHS
BINDING NUMBERS AND FRACTIONAL (g, f, n)-CRITICAL GRAPHS
Journal of applied mathematics & informatics. 2016. Sep, 34(5_6): 435-441
  • Received : November 28, 2015
  • Published : September 30, 2016
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ZHOU, SIZHONG
SUN, ZHIREN

Abstract
Let G be a graph, and let g, f be two nonnegative integer-valued 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.
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