Longest paths in digraphs

Abstract

In this paper, we give a sufficient condition on the degrees of the vertices of a digraph to insure the existence of a path of given length, and we characterize the extremal graphs.

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References

  1. [1]

    C. Berge, Graphs and hypergraphs, North Holland, Amsterdam, 1973.

    MATH  Google Scholar 

  2. [2]

    J. C. Bermond, A. Germa, M. C. Heydemann andD. Sotteau, Chemins et circuits dans les graphes orientés, Proc. Coll. Montréal, 1979.Annals of Discrete Mathematics 8 (1980), 293–309.

    MATH  MathSciNet  Article  Google Scholar 

  3. [3]

    J. C. Bermond, On hamiltonian walks, Proc. 5th British Combinatorial Conference, Aberdeen, 1975,Congressus Numerantium 15,Utilitas Math. Publ., 41–51.

  4. [4]

    J. C. Bermond andC. Thomassen, Cycles in digraphs, a survey,J. Graph Theory,5 (1981), 1–43.

    MATH  MathSciNet  Google Scholar 

  5. [5]

    A. Ghouila-Houri, Flots et tensions dans un graphe,Ann. Scien. Ec. Norm. Sup.,81 (1964), 317–327.

    MathSciNet  Google Scholar 

  6. [6]

    M. C. Heydemann,Thesis, Université Paris-Sud.

  7. [7]

    M. C. Heydemann, On cycles and paths in digraphs,Discrete Math. 31 (1980), 217–219.

    MATH  Article  MathSciNet  Google Scholar 

  8. [8]

    B. Jackson, Long paths and cycles in oriented graphs,J. Graph. Theory,5 (1981), 145–157,

    MATH  MathSciNet  Google Scholar 

  9. [9]

    M. Las Vergnas, Sur les arborescences dans un graphe orientéDiscrete Math. 15 (1976), 27–39.

    MATH  Article  MathSciNet  Google Scholar 

  10. [10]

    C. Thomassen, Long cycles in digraphs,Proc. London Math. Soc. to appear.

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Bermond, J.C., Germa, A., Heydemann, M.C. et al. Longest paths in digraphs. Combinatorica 1, 337–341 (1981). https://doi.org/10.1007/BF02579454

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AMS subject classification (1980)

  • 05 C 20
  • 05 C 38