Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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TIGHT TOUGHNESS CONDITION FOR FRACTIONAL (g, f, n)-CRITICAL GRAPHS

  • Gao, Wei (School of Information Science and Technology Yunnan Normal University) ;
  • Liang, Li (School of Information Science and Technology Yunnan Normal University) ;
  • Xu, Tianwei (School of Information Science and Technology Yunnan Normal University) ;
  • Zhou, Juxiang (Key Laboratory of Educational Informatization for Nationalities Ministry of Education Yunnan Normal University)
  • Received : 2012.09.02
  • Published : 2014.01.01
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Abstract

A graph G is called a fractional (g, f, n)-critical graph if any n vertices are removed from G, then the resulting graph admits a fractional (g, f)-factor. In this paper, we determine the new toughness condition for fractional (g, f, n)-critical graphs. It is proved that G is fractional (g, f, n)-critical if $t(G){\geq}\frac{b^2-1+bn}{a}$. This bound is sharp in some sense. Furthermore, the best toughness condition for fractional (a, b, n)-critical graphs is given.

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References

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  1. Toughness Condition for a Graph to Be a Fractional(g,f,n)-Critical Deleted Graph vol.2014, 2014, https://doi.org/10.1155/2014/369798
  2. Some Existence Theorems on All Fractional (g, f)-factors with Prescribed Properties vol.34, pp.2, 2018, https://doi.org/10.1007/s10255-018-0753-y