Skip to main content
Log in

Quasi-random graphs

  • Published:
Combinatorica Aims and scope Submit manuscript

Abstract

We introduce a large equivalence class of graph properties, all of which are shared by so-called random graphs. Unlike random graphs, however, it is often relatively easy to verify that a particular family of graphs possesses some property in this class.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. N. Alon andF. R. K. Chung, Explicit constructions of linear-sized tolerant networksDiscrete Math.,72 (1988), 15–20.

    Google Scholar 

  2. B. Bollobás,Random Graphs, Academic Press, New York, 1985.

    Google Scholar 

  3. B. Bollobás andA. Thomason, Graphs which contain all small graphs,European J. Comb. 2 (1981), 13–15.

    Google Scholar 

  4. D. A. Burgess, On character sums and primitive roots,Proc. London Math. Soc. 12 (1962), 179–192.

    Google Scholar 

  5. P.Erdős and A.Hajnal, On spanned subgraphs of graphs,Beitrage zur Graphentheorie und deren Anwendungen, Kolloq. Oberhof (DDR), (1977), 80–96.

  6. P. Erdős andJ. Spencer,Probabilistic Methods in Combinatorics, Akadémiai Kiadó, Budapest, 1974.

    Google Scholar 

  7. P. Frankl andR. L. Graham, Intersection theorems for vector spaces,European J. Comb. 6 (1985), 183–187.

    Google Scholar 

  8. P.Frankl, V.Rödl and R. M.Wilson, The number of submatrices of given type in a Hadamard matrix and related results (to appear).

  9. P. Frankl andR. M. Wilson, Intersection theorems with geometric consequences,Combinatorica 1 (1981), 357–368.

    Google Scholar 

  10. Z. Füredi andJ. Komlós, The eigenvalues of random symmetric matrices,Combinatorica 1 (1981), 233–241.

    Google Scholar 

  11. F. R. Gantmacher,Matrix Theory, Vol. 1, Chelsea, New York, 1977.

    Google Scholar 

  12. R. L. Graham andJ. H. Spencer, A constructive solution to a tournament problem,Canad. Math. Bull. 14 (1971), 45–48.

    Google Scholar 

  13. F.Juhász, On the spectrum of a random graph,Colloq. Math. Soc. János Bolyai 25,Algebraic Methods in Graph Theory, Szeged (1978), 313–316.

  14. H. L. Montgomery, Topics in Multiplicative Number Theory,Lecture Notes in Math. 227, Springer-Verlag, New York, 1971.

    Google Scholar 

  15. E. M. Palmer,Graphical Evolution, Wiley, New York, 1985.

    Google Scholar 

  16. V. Rödl, On the universality of graphs with uniformly distributed edges,Discrete Math. 59 (1986), 125–134.

    Google Scholar 

  17. A. Thomason, Random graphs, strongly regular graphs and pseudo-random graphs, in Surveys in Combinatorics 1987 (C. Whitehead, ed.)LMS Lecture Notes Series 123, Cambridge Univ. Press, Cambridge, (1987), 173–196.

    Google Scholar 

  18. A.Thomason, Random graphs, strongly regular graphs and pseudo-random graphs, in Surveys

  19. A.Thomason, Pseudo-random graphs, in Proceedings of Random Graphs, Poznań 1985 (M. Karonski, ed.)Annals of Discrete Math. 33 (1987), 307–331.

  20. A.Weil, Sur les courbes algébrique et les variétés qui s'en déduisent,Actualités Sci. Ind. No. 1041 (1948).

  21. R. M. Wilson, Cyclotomy and difference families in abelian groups,J. Number Th. 4 (1972), 17–47.

    Google Scholar 

  22. R. M.Wilson, Constructions and uses of pairwise balanced designs, in Combinatorics (M. Hall, Jr. and J. H. van Lint, eds.),Math. Centre Tracts 55, Amsterdam (1974), 18–41.

  23. F. R. K.Chung and R. L.Graham, Quasi-random hypergraphs,to appear.

  24. S. W.Graham and C.Ringrose,to appear.

Download references

Author information

Authors and Affiliations

Authors

Additional information

The authors wish to express their appreciation to N. Pippenger for several useful comments on an early draft of this paper.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chung, F.R.K., Graham, R.L. & Wilson, R.M. Quasi-random graphs. Combinatorica 9, 345–362 (1989). https://doi.org/10.1007/BF02125347

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02125347

AMS subject classification (1980)

Navigation