Bulletin of the Korean Mathematical Society (대한수학회보)

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DEGREE CONDITIONS AND FRACTIONAL k-FACTORS OF GRAPHS

  • Zhou, Sizhong (School of Mathematics and Physics Jiangsu University of Science and Technology)
  • Received : 2009.07.30
  • Published : 2011.03.31
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Abstract

Let k $\geq$ 1 be an integer, and let G be a 2-connected graph of order n with n $\geq$ max{7, 4k+1}, and the minimum degree $\delta(G)$ $\geq$ k+1. In this paper, it is proved that G has a fractional k-factor excluding any given edge if G satisfies max{$d_G(x)$, $d_G(y)$} $\geq$ $\frac{n}{2}$ for each pair of nonadjacent vertices x, y of G. Furthermore, it is showed that the result in this paper is best possible in some sense.

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References

  1. J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, American Elsevier Publishing Co., Inc., New York, 1976.
  2. T. Iida and T. Nishimura, An Ore-type condition for the existence of k-factors in graphs, Graphs Combin. 7 (1991), no. 4, 353-361. https://doi.org/10.1007/BF01787640
  3. Z. Li, G. Yan, and X. Zhang, On fractional (g; f)-deleted graphs, Math. Appl. (Wuhan) 16 (2003), no. 1, 148-154.
  4. G. Liu and L. Zhang, Fractional (g; f)-factors of graphs, Acta Math. Sci. Ser. B Engl. Ed. 21 (2001), no. 4, 541-545.
  5. G. Liu and L. Zhang, Toughness and the existence of fractional k-factors of graphs, Discrete Math. 308 (2008), no. 9, 1741-1748. https://doi.org/10.1016/j.disc.2006.09.048
  6. T. Nishimura, A degree condition for the existence of k-factors, J. Graph Theory 16 (1992), no. 2, 141-151. https://doi.org/10.1002/jgt.3190160205
  7. C. Wang, A degree condition for the existence of k-factors with prescribed properties, Int. J. Math. Math. Sci. 2005 (2005), no. 6, 863-873. https://doi.org/10.1155/IJMMS.2005.863
  8. J. Yu and G. Liu, Fractional k-factors of graphs, Gongcheng Shuxue Xuebao 22 (2005), no. 2, 377-380.
  9. S. Zhou, Independence number, connectivity and (a; b; k)-critical graphs, Discrete Math. 309 (2009), no. 12, 4144-4148. https://doi.org/10.1016/j.disc.2008.12.013
  10. S. Zhou, Some new sufficient conditions for graphs to have fractional k-factors, Int. J. Comput. Math. 88 (2011), no. 3, 484-490. https://doi.org/10.1080/00207161003681286
  11. S. Zhou and J. Jiang, Notes on the binding numbers for (a; b; k)-critical graphs, Bull. Austral. Math. Soc. 76 (2007), no. 2, 307-314. https://doi.org/10.1017/S000497270003968X
  12. S. Zhou and H. Liu, Neighborhood conditions and fractional k-factors, Bull. Malays. Math. Sci. Soc. (2) 32 (2009), no. 1, 37-45.
  13. S. Zhou and Q. Shen, On fractional (f; n)-critical graphs, Inform. Process. Lett. 109 (2009), no. 14, 811-815. https://doi.org/10.1016/j.ipl.2009.03.026

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