Disjoint cycles in digraphs

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.

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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.

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Dedicated to Paul Erdős on his seventieth birthday

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

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AMS subject classification (1980)

  • 05 C 20
  • 05 C 38