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

Li Liang|Wei Gao|Tianwei Xu|Juxiang Zhou
대한수학회 (The Korean Mathematical Society)|2014.01|대한수학회지 (Journal of the KMS)|제51권 제1호|pp. 55-65

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참고문헌

키워드

toughnessbfractional (gf)-factorfn)-critical graphfractional (an)-critical graph.
주제분류수학

초록

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.

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) ≥ 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.

참고문헌 (10)

  1. Q. Bian, "On toughness and fractional f-factors", Ars Combin, 87, pp.175~180 (2008)
  2. J. A. Bondy, "Graph Theory" (2008), Spring
  3. V. Chvatal, "Tough graphs and Hamiltonian circuits", Discrete Math, 5, pp.215~228 (1973)
  4. G. Liu, "Fractional (g, f)-factors of graphs", Acta Math. Sci. Ser. B Engl. Ed, 21(4), pp.541~545 (2001)
  5. G. Liu, "Characterizations of maximum fractional (g, f)-factors of graphs", Discrete Appl. Math, 156(12), pp.2293~2299 (2008)
  6. G. Liu, "Toughness and the existence of fractional k-factors of graphs", Discrete Math, 308(9), pp.1741~1748 (2008)
  7. S. Liu, "On toughness and fractional (g, f, n)-critical graphs", Inform. Process. Lett, 110(10), pp.378~382 (2010)
  8. S. Liu, "Toughness and existence of fractional (g, f)-factors in graphs", Ars Combin, 93, pp.305~311 (2009)
  9. S. Zhou, "Independence number, connectivity and (a, b, k)-critical graphs", Discrete Math, 309(12), pp.4144~4148 (2009)
  10. S. Zhou, "A sufficient condition for a graph to be an (a, b, k)-critical graph", Int. J. Comput. Math, 87(10), pp.2202~2211 (2010)

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