Skip to main content
SpringerLink
Log in

Component structure in the evolution of random hypergraphs

  • Published:
Combinatorica Aims and scope Submit manuscript

Abstract

The component structure of the most general random hypergraphs, with edges of differen sizes, is analyzed. We show that, as this is the case for random graphs, there is a “double jump” in the probable and almost sure size of the greatest component of hypergraphs, when the average vertex degree passes the value 1.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Ajtai, J. Komlós andE. Szemerédi, The longest path in a random graph,Combinatorica,1 (1981), 1–12.

    Article  MATH  MathSciNet  Google Scholar 

  2. C. Berge,Graphes et Hypergraphes, Dunod, Paris, (1970).

    MATH  Google Scholar 

  3. C. Berge,Introduction à la Theorie des Hypergraphes, Le presse de l’Université de Montréal, Seminaire de Math. Superieur, été 1971.

  4. B. Bollobás andP. Erdős, Cliques in random graphs,Math. Proc. Camb. Phil. Soc.,80 (1976), 419–427.

    Article  MATH  Google Scholar 

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

    Google Scholar 

  6. P. Erdős,The Art of Counting, Selected Writings, MIT Press, Cambridge/Massachusetts and London/England, 1973.

    Google Scholar 

  7. P. Erdős andJ. Spencer,Probabilistic Methods in Combinatorics. Academic Press, New York, 1974.

    Google Scholar 

  8. W. Fernandez de la Vega, Sur la cardinalité maximum des couplages d’hypergraphes aléatoire uniformes,Discrete Math. 40, (1982), 315–318.

    Article  MATH  MathSciNet  Google Scholar 

  9. J. Schmidt andE. Shamir, A threshold for perfect matchings ind-pure random hypergraphs,Discrete Math.,45 (1983), 287–295.

    Article  MATH  MathSciNet  Google Scholar 

  10. J. Schmidt-Pruzan, E. Shamir, andE. Upfal, Random hypergraph coloring algorithms and the weak chromatic number,Journal of Graph Theory (to appear), (Preliminary version: Technical Report (CS83-09) Dept. Appl. Math. Weizmann Inst. of Sc. Rehovot Israel).

  11. J. Schmidt-Pruzan, Probabilistic analysis of strong hypergraph coloring algorithms and the strong chromatic number.Submitted to Discrete Math., (Preliminary version: Technical Report (CS83-10) Dept. Appl. Math. Weizmann Inst. of Sc. Rehovot Israel).

  12. I. Tomescu, Asymptotical estimations for the number of cliques of uniform hypergraphs,Annals of Discrete Math.,11,Studies on graphs and Discrete Programming (1981), (Edited by P. Hansen), North-Holland Publishing Comp., 345–358.

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, The Weizmann Institute of Science, 76100, Rehovot, Israel

    Jeanette Schmidt-Pruzan & Eli Shamir

  2. The Institute of Mathematics and Comp. Sci., The Hebrew University, Jerusalem, Israel

    Jeanette Schmidt-Pruzan & Eli Shamir

Authors
  1. Jeanette Schmidt-Pruzan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Eli Shamir
    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

Schmidt-Pruzan, J., Shamir, E. Component structure in the evolution of random hypergraphs. Combinatorica 5, 81–94 (1985). https://doi.org/10.1007/BF02579445

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02579445

AMS subject classification (1980)

Search

Navigation