Skip to main content
Log in

On graphs with randomly deleted edges

  • Published:
Acta Mathematica Academiae Scientiarum Hungarica Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. A. Rényi, Some remarks on the theory of trees,Publ. Math. Inst. Hung. Acad. Sci.,4 (1959), 73–85.

    Google Scholar 

  2. P. Erdős andA. Rényi, On the evolution of random graphs,Publ. Math. Inst. Hung. Acad. Sci.,5 (1960), 17–61.

    Google Scholar 

  3. A. K. Kelmans, On the connectedness of random graphs,Avtomatika i Telemehanika (translated asAutomation and Remote Control),28 (1967), 98–116.

    Google Scholar 

  4. V. E. Stepanov, Combinatorial algebra and random graphs,Teoriya veroyatnostei i ee primeneniya,14 (1969), 393–420.

    Google Scholar 

  5. A. K. Kelmans, Asymptotic formulas for the probability ofk-connectedness of random graphs,Teoriya veroyatnosteí i ee primeneniya,17 (1972), 253–265.

    Google Scholar 

  6. M. V. Lomonosov andV. P. Polesskií, The lower bound for networks reliability,Problemy Peredachi Informacii,8 (1972), 47–53.

    Google Scholar 

  7. M. V. Lomonosov andV. P. Polesskií, On the maximum of the probability of connectivity,Problemy Peredachi Informacii,8 (1972), 68–73.

    Google Scholar 

  8. G. A. Margulis, Probabilistic characteristics of graphs with large connectivity,Problemy Peredachi Informacii (translated asProblems of Information Transmission),10 (1974), 101–108.

    Google Scholar 

  9. H. Frank andI. Frish, Analysis and Design of Survivable Networks,IEEE Transactions on Communication Technology, v. Com.-18, No5 (1970), 501–549.

    Google Scholar 

  10. R. S. Wilkow, Analisis and Design of Reliable Computer Networks,IEEE Transactions on Communications, v. COM-20, No3 (1972), 660–678.

    Google Scholar 

  11. A. K. Kelmans, On properties of the characteristic polynomial of a graph,Kibernetiku na sluźbu kommunizmu, v. 4, Gosenergoizdat (Moscow, 1967), 27–41.

    Google Scholar 

  12. A. K. Kelmans andV. M. Chelnokov, A certain polynomial of a graph and graphs with an extremal number of trees,J. Combinatorial Theory,16(B) (1974), 187–214.

    Google Scholar 

  13. A. K. Kelmans, Operations over graphs increasing the number of their spanning trees, in:Issledovaniya po discretnoy optimizacii, Nauka (Moscow, 1976), 406–424.

    Google Scholar 

  14. A. K. Kelmans, Comparison of graphs by their number of spanning trees,Discrete Mathematics,16 (1976), 241–261.

    Google Scholar 

  15. A. K. Kelmans, On analysis and synthesis of random graphs, in: Nadeźnost i stabilnost informacionnyh ustroístv i sistem, Znanie, (Kiev, 1975), 3–4.

    Google Scholar 

  16. A. K. Kelmans, The graph with the maximum probability of remaining connected depends upon the edge-removal probability,Graph Theory Newsletter,9(1) (1979), 2–3.

    Google Scholar 

  17. F. Harary,Graph Theory, Addison-Wesley (Reading, Mass., 1969).

    Google Scholar 

  18. A. K. Kelmans, The number of trees in a graph I, II,Avtomatika i Telemehanika,26 (1965), 2194–2204 and27 (1966), 56–65.

    Google Scholar 

  19. A. K. Kelmans, Graphs with extremal number of spanning trees,Journal of Graph Theory,4 (1980), 119–122.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kelmans, A.K. On graphs with randomly deleted edges. Acta Mathematica Academiae Scientiarum Hungaricae 37, 77–88 (1981). https://doi.org/10.1007/BF01904874

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01904874

Navigation