Disjoint cycles in digraphs

Combinatorica volume 3, pages393–396(1983)Cite this article

Abstract

We show that, for each natural numberk, these exists a (smallest) natural numberf(k) such that any digraph of minimum outdegree at leastf(k) containsk disjoint cycles. We conjecture thatf(k)=2k−1 and verify this fork=2 and we show that, for eachk≧3, the determination off(k) is a finite problem.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

US$ 39.95

Tax calculation will be finalised during checkout.

References

  1. [1]

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

    MATH  MathSciNet  Google Scholar 

  2. [2]

    K. Corrádi andA. Hajnal, On the maximal number of independent circuits of a graph,Acta Math. Acad. Sci. Hungar 14 (1963), 423–443.

    MATH  Article  MathSciNet  Google Scholar 

  3. [3]

    G. A. Dirac andP. Erdős, On the maximal number of independent circuits in a graph,Acta Math. Acad. Sci. Hungar 14 (1963), 79–94.

    MATH  Article  MathSciNet  Google Scholar 

  4. [4]

    P. Erdős andL. Pósa, On independent circuits contained in a graph,Canad. J. Math. 17 (1965), 347–352.

    MathSciNet  Google Scholar 

  5. [5]

    S. Fortune, J. Hopcroft andJ. Wyllie, The directed subgraph homeomorphism problem,Theor. Comput. Sci. 10 (1980), 111–121.

    MATH  Article  MathSciNet  Google Scholar 

  6. [6]

    R. Häggkvist, Equicardinal disjoint cycles in sparse graphs,to appear.

  7. [7]

    N. Robertson andP. D. Seymour,to appear.

  8. [8]

    C. Thomassen, Even cycles in digraphs,to appear.

  9. [9]

    C. Thomassen, Girth in graphs,J. Comb. Th., to appear.

Download references

Author information

Affiliations

  1. Matematisk Institut Danmarks Teknishe Hojskole, Bygning 303, 2800, Lyngby, Danmark

    Carsten Thomassen

Authors
  1. Carsten Thomassen
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Dedicated to Paul Erdős on his seventieth birthday

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Thomassen, C. Disjoint cycles in digraphs. Combinatorica 3, 393–396 (1983). https://doi.org/10.1007/BF02579195

Download citation

AMS subject classification (1980)

  • 05 C 20
  • 05 C 38