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Notes on Fractional (1,f)-Odd Factors of Graphs

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Frontiers in Algorithmics (FAW 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4613))

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Abstract

Let G be a simple graph and f an odd integer-valued function defined on V(G). A spanning subgraph F of G is called a fractional (1, f)-odd factor if d F (v) ∈ {1, 3, ⋯ , f(v)} for all v ∈ V(G), where d F (v) is the fractional degree of v in F. In this paper, we discuss the existence for a graph to have a fractional (1,f)-odd-factor. A necessary and sufficient condition for a tree to have a fractional (1,f)-odd factor is given.

The work is supported by NNSF (10471078) of China and RFDP (20040422004), Promotional Foundation (2005BS01016) for Middle-aged or Young Scientists of Shandong Province, DRF and UF(XJ0609)of QFNU.

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References

  1. Amahashi, A.: On factors with all degrees odd. Graphs and Comb. 1, 111–114 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  2. Ansteen, R.P.: An algorithmic proof Tutte’s f-factors of graphs. J. Algor., 112–131 (1985)

    Google Scholar 

  3. Bondy, J.A., Murty, U.S.R.: Graph Theory with Applications. MacMillan Press, London (1976)

    Google Scholar 

  4. Chen, C.P., Wang, J.F.: Factors in graphs with odd-cycle property. Discrete Math. 112, 29–40 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  5. Cui, Y., Kano, M.: Some Results on Odd factors of graph. J. Graph Theory 12(3), 327–323 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  6. Kano, M., Katona, G.Y.: Odd subgraphs and matchings. Discrete Math. 250, 265–272 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  7. Liu, G.Z., Zhang, L.J.: Fractional (g, f)-factors of graphs. Acta Math. Scientia 21B4, 541–545 (2001)

    Google Scholar 

  8. Scheinerman, E.R., Ullman, D.H.: Fractional Graph Theory. John Wiley and Sons, Inc., New York (1997)

    MATH  Google Scholar 

  9. Topp, J., Vestergaard, P.D.: Odd Factors of a graph. Graphs and Comb. 9, 371–381 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  10. Yu, Q.L., Zhang, Z.: Extremal properties of (1, f)-odd factors in graphs. Ars Comb. (to appear)

    Google Scholar 

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Authors and Affiliations

  1. School of Computer Science, Qufu Normal University, Ri-zhao, Shandong, 276826, P.R. China

    Jiguo Yu

  2. School of Mathematics and System Science, Shandong University, Ji-nan, Shandong, 250100, P.R. China

    Guizhen Liu

Authors
  1. Jiguo Yu
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  2. Guizhen Liu
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Franco P. Preparata Qizhi Fang

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© 2007 Springer-Verlag Berlin Heidelberg

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Yu, J., Liu, G. (2007). Notes on Fractional (1,f)-Odd Factors of Graphs. In: Preparata, F.P., Fang, Q. (eds) Frontiers in Algorithmics. FAW 2007. Lecture Notes in Computer Science, vol 4613. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73814-5_30

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  • DOI: https://doi.org/10.1007/978-3-540-73814-5_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73813-8

  • Online ISBN: 978-3-540-73814-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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