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

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

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...

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Veröffentlicht in:Journal of the Korean Mathematical Society 2014, 51(1), , pp.55-65
Hauptverfasser: Gao, Wei, Liang, Li, Xu, Tianwei, Zhou, Juxiang
Format: Artikel
Sprache:eng
Schlagworte:
수학
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Zusammenfassung: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. KCI Citation Count: 32
ISSN:0304-9914
2234-3008
DOI:10.4134/JKMS.2014.51.1.055