On the connectivity of randomm-orientable graphs and digraphs

Combinatorica volume 2, pages347–359(1982)Cite this article

Abstract

We consider graphs and digraphs obtained by randomly generating a prescribed number of arcs incident at each vertex.

We analyse their almost certain connectivity and apply these results to the expected value of random minimum length spanning trees and arborescences.

We also examine the relationship between our results and certain results of Erdős and Rényi.

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]

    P. Erdős andA. Rényi, On Random Graphs I,Publ. Math. Debrecen,6 (1959), 290–297.

    MathSciNet  Google Scholar 

  2. [2]

    P. Erdős andA. Rényi, On the Evolution of Random Graphs,Magyar Tud. Akad. Mat. Kut. Int. Közl. 5 (1960), 17–61.

    Google Scholar 

  3. [3]

    P. Erdős andA. Rényi, On the Strength of Connectedness of a Random Graph,Acta. Math. Acad. Sci. Hungar.,12 (1961), 261–267.

    Article  MathSciNet  Google Scholar 

  4. [4]

    L. Katz, Probability of Indecomposability of a Random Mapping Function,Annals of Mathematical Statistics,25 (1955), 512–517.

    Google Scholar 

  5. [5]

    M. Kruskal, The Expected Number of Components under a Random Mapping Function, American Mathematical Monthly,61 (1954), 392–397.

    MATH  Article  MathSciNet  Google Scholar 

  6. [6]

    D. W. Walkup, On the Expected Value of a Random Assignment Problem,SIAM Journal on Computing,8 (1979), 440–442.

    MATH  Article  MathSciNet  Google Scholar 

  7. [7]

    T. I. Fenner andA. M. Frieze, On the existence of Hamiltonian cycles in a class of random graphs,to appear in Discr. Math.

  8. [8]

    A. Frank andA. Gyárfás, How to orient the edges of a graph?, 1976 Colloq. Math. Soch. J. Bolyai18 (1978), 353–364.

    Google Scholar 

Download references

Author information

Affiliations

  1. Dept. of Computer Science Birkbeck College, University of London, WC1E 7HX, London, England

    T. I. Fenner

  2. Dept. of Computer Science and Statistics, Queen Mary College, E1 4NS, London, England

    A. M. Frieze

Authors
  1. T. I. Fenner
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. M. Frieze
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Fenner, T.I., Frieze, A.M. On the connectivity of randomm-orientable graphs and digraphs. Combinatorica 2, 347–359 (1982). https://doi.org/10.1007/BF02579431

Download citation

AMS subject classification (1980)

  • 05 C 40
  • 60 C 05