Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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NOTE ON CONNECTED (g, f)-FACTORS OF GRAPHS

  • Zhou, Sizhong (School of Mathematics and Physics, Jiangsu University of Science and Technology) ;
  • Wu, Jiancheng (School of Mathematics and Physics, Jiangsu University of Science and Technology) ;
  • Pan, Quanru (School of Mathematics and Physics, Jiangsu University of Science and Technology)
  • Received : 2009.09.22
  • Accepted : 2010.02.16
  • Published : 2010.05.30
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Abstract

In this note we present a short proof of the following result by Zhou, Liu and Xu. Let G be a graph of order n, and let a and b be two integers with 1 $\leq$ a < b and b $\geq$ 3, and let g and f be two integer-valued functions defined on V(G) such that a $\leq$ g(x) < f(x) $\leq$ b for each $x\;{\in}\;V(G)$ and f(V(G)) - V(G) even. If $n\;{\geq}\;\frac{(a+b-1)^2+1}{a}$ and $\delta(G)\;{\geq}\;\frac{(b-1)n}{a+b-1}$,then G has a connected (g, f)-factor.

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References

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