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Degree and stability number condition for the existence of connected factors in graphs

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Abstract

Let G be a graph with vertex set V(G) and let f be a nonnegative integer-valued function defined on V(G). A spanning subgraph F of G is called an f-factor if d F (x)=f(x) for every x∈V(F). In this paper we present some sufficient conditions for the existence of f-factors, connected (f,f+1)-factors and connected (f−2,f)-factors in graphs. The conditions involve the minimum degree and the stability number of graph G. Therefore we prove that the conjecture in Cai and Liu (Ars Comb. to appear, 2008) is true in some sense.

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References

  1. Bondy, J.A., Murty, U.S.R.: Graph Theory with Applications. Macmillan, London (1976)

    Google Scholar 

  2. Cai, J., Liu, G.: Stability number and f-factors in K 1,n -free graphs. Ars Comb. (2008, to appear)

  3. Cai, J., Liu, G.: Stability number and fractional f-factors in graphs. Ars Comb. 80, 141–146 (2006)

    MATH  MathSciNet  Google Scholar 

  4. Cai, J., Liu, G.: Binding number and Hamiltonian (g,f)-factors in graphs. J. Appl. Math. Comput. 25(1–2), 383–388 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  5. Katerinis, P., Woodall, D.R.: Binding numbers of graphs and the existence k-factors. Q. J. Math. 38, 221–228 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  6. Li, G., Xu, Y., Chen, C., Liu, Z.: On connected (g,f+1)-factors in graphs. Combinatorica 25(4), 393–405 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  7. Liu, G.: (g,f)-factors and factorizations in graphs. Acta Math. Sin. 37, 230–237 (1994)

    MATH  Google Scholar 

  8. Nishimura, T.: Independence number, connectivity, and r-factors. J. Graph Theory 13, 63–69 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  9. Tutte, W.T.: The factor of graphs. Can. T. Math. 4, 314–328 (1952)

    MATH  MathSciNet  Google Scholar 

  10. Zhu, Y., Liu, G.: Some results on binding number and fractional perfect matching. J. Appl. Math. Comput. 25(1–2), 339–344 (2007)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Mathematics and Information Science, Weifang University, Weifang, 261061, China

    Jiansheng Cai

  2. School of Mathematics and System Sciences, Shandong University, Jinan, 250100, China

    Guizhen Liu

Authors
  1. Jiansheng Cai
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  2. Guizhen Liu
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Corresponding author

Correspondence to Jiansheng Cai.

Additional information

This work is supported by the National Natural Science Foundation (60673047).

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Cai, J., Liu, G. Degree and stability number condition for the existence of connected factors in graphs. J. Appl. Math. Comput. 29, 349–356 (2009). https://doi.org/10.1007/s12190-008-0135-3

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  • DOI: https://doi.org/10.1007/s12190-008-0135-3

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