TIGHT TOUGHNESS CONDITION FOR FRACTIONAL (g, f, n)-CRITICAL GRAPHS

Title & Authors
TIGHT TOUGHNESS CONDITION FOR FRACTIONAL (g, f, n)-CRITICAL GRAPHS
Gao, Wei; Liang, Li; Xu, Tianwei; Zhou, Juxiang;

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 $\small{t(G){\geq}\frac{b^2-1+bn}{a}}$. This bound is sharp in some sense. Furthermore, the best toughness condition for fractional (a, b, n)-critical graphs is given.
Keywords
toughness;fractional (g, f)-factor;fractional (g, f, n)-critical graph;fractional (a, b, n)-critical graph;
Language
English
Cited by
1.
Toughness Condition for a Graph to Be a Fractional(g,f,n)-Critical Deleted Graph, The Scientific World Journal, 2014, 2014, 1
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