Degree and local connectivity in digraphs


It is shown that there is a digraphD of minimum outdegree 12m and\(\mathop {\max }\limits_{x \ne y} \) μ(x, y; D)=11m, but every digraphD of minimum outdegreen contains verticesxy withλ(x, y; D)≧n−1, whereμ(x, y; D) andλ(x, y; D) denote the maximum number of openly disjoint and edge-disjoint paths, respectively.

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


  1. [1]

    R. P. Gupta, On flows in pseudosymmetric networks,J. Siam Appl. Math. 14 (1966), 215–225.

    MATH  Article  Google Scholar 

  2. [2]

    R. Halin,Graphentheorie I, Wissenschaftliche Buchgesellschaft, Darmstadt 1980.

    Google Scholar 

  3. [3]

    Y. O. Hamidoune, An application of connectivity theory in graphs to factorizations of elements in groups,Europ. J. Combinatorics 2 (1981), 349–355.

    MATH  MathSciNet  Google Scholar 

  4. [4]

    L. Lovász, Connectivity in digraphs,J. Combinatorial Theory (B) 15 (1973), 174–177.

    MATH  Article  Google Scholar 

  5. [5]

    W. Mader, Existenzn-fach zusammenhängender Teilgraphen in Graphen genügend großer Kantendichte,Abh. Math. Sem. Universität Hamburg 37 (1972), 86–97.

    MATH  MathSciNet  Google Scholar 

  6. [6]

    W. Mader, Hinreichende Bedingungen für die Existenz von Teilgraphen, die zu einem vollständigen Graphen homöomorph sind,Math. Nachr. 53 (1972), 145–150.

    MATH  MathSciNet  Google Scholar 

  7. [7]

    W. Mader, Grad und lokaler Zusammenhang in endlichen Graphen,Math. Ann. 205 (1973), 9–11.

    MATH  Article  MathSciNet  Google Scholar 

  8. [8]

    L. Mirsky,Transversal theory, New York, London, Academic Press 1971.

    Google Scholar 

  9. [9]

    C. Thomassen, Even cycles in directed graphs,to appear in European Journal of Combinatorics.

Download references

Author information



Rights and permissions

Reprints and Permissions

About this article

Cite this article

Mader, W. Degree and local connectivity in digraphs. Combinatorica 5, 161–165 (1985).

Download citation

AMS subject classification (1980)

  • 05 C 40
  • 05 C 20
  • 05 C 38