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Odd factors of a graph

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Abstract

LetG be a graph and letf be a function defined on V(G) such that f(x) is a positive odd integer for everyx ɛ V(G). A spanning subgraphF ofG is called a [l,f]-odd factor of G if dF(x) ɛ {1,3,2026, f(x)} for every x ɛV(G), whered F (x) denotes the degree of x inF. We discuss several conditions for a graphG to have a [1,f]-odd factor.

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References

  1. Akiyama, J., Kano, M.: Factors and factorizations of graphs — a survey. J. Graph Theory9, 1–42 (1985)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  3. Beineke, L.W., Plummer, M.D.: On the 1-factors of a nonseparable graph. J. Comb. Theory2, 285–289 (1967)

    Article  MATH  MathSciNet  Google Scholar 

  4. Chartrand, G., Polimeni, A.D., Stewart, M.J.: The existence of 1-factors in line graphs, squares, and total graphs. Indag. Math.35, 228–232 (1973)

    MathSciNet  Google Scholar 

  5. Chungphaisan, V.: Factors of graphs and degree sequences. Nanta Math.9, 41–49 (1976)

    MATH  MathSciNet  Google Scholar 

  6. Clarke, F.H.: A graph polynomial and its applications. Discrete Math.3, 305–313 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  7. Jackson, B., Whitty, R.W.: A note concerning graphs with unique f-factors. J. Graph Theory13, 577–580 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  8. Kotzig, A.: On the theory of finite graphs with a linear factor I, II, III. Mat. Fyz. Cas.9, 73–91 (1959)

    MATH  Google Scholar 

  9. Las Vergnas, M.: A note on matchings in graphs. Cahiers Centre Études Rech. Opér.17, 257–260 (1975)

    MATH  MathSciNet  Google Scholar 

  10. Sumner, D.P.: Graphs with 1-factors. Proc. Amer. Math. Soc.42, 8–17 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  11. Sumner, D.P.: 1-factors and antifactor sets. J. London Math. Soc.13, 351–359 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  12. Tutte, W.T.: The factorizations of linear graphs. J. London Math. Soc.22, 107–111 (1947)

    Article  MATH  MathSciNet  Google Scholar 

  13. Tutte, W.T.: Graph factors. Combinatorica1, 79–97 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  14. Yuting, C., Kano, M.: Some results on odd factors of graphs. J. Graph Theory12, 327–333 (1988)

    Article  MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. Faculty of Applied Physics and Mathematics, Technical University of Gdańsk, Majakowskiego 11/12, 80-952, Gdańsk, Poland

    Jerzy Topp

  2. Department of Mathematics and Computer Science, Aalborg University, Frederik Bajers Vej 7, DK-9220, Aalborg, Denmark

    Preben D. Vestergaard

Authors
  1. Jerzy Topp
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  2. Preben D. Vestergaard
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Topp, J., Vestergaard, P.D. Odd factors of a graph. Graphs and Combinatorics 9, 371–381 (1993). https://doi.org/10.1007/BF02988324

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  • DOI: https://doi.org/10.1007/BF02988324

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