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TIGHT TOUGHNESS CONDITION FOR FRACTIONAL (g,f,n)-CRITICAL GRAPHS
Wei Gao,Li Liang,Tianwei Xu,Juxiang Zhou 대한수학회 2014 대한수학회지 Vol.51 No.1
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) ≥ b3-1+bn/a. This bound is sharp in some sense. Furthermore, the best toughness condition for fractional (a, b,n)-critical graphs is given.
TIGHT TOUGHNESS CONDITION FOR FRACTIONAL (g, f, n)-CRITICAL GRAPHS
Gao, Wei,Liang, Li,Xu, Tianwei,Zhou, Juxiang Korean Mathematical Society 2014 대한수학회지 Vol.51 No.1
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.