Skip to main content
SpringerLink
Log in
Book cover

The Mathematics of Paul Erdös I pp 280–310Cite as

Games, Randomness and Algorithms

  • Chapter

Part of the book series: Algorithms and Combinatorics ((AC,volume 13))

Abstract

The object of this 50% survey and 50% “theorem-proof” paper is to demonstrate recent developments of some of the ideas initiated by Erdős [17], [18], Erdős and Selfridge [20], Erdős and Lovász [19] and Erdős and Chvátal [15].

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. N. Alon, and J. Spencer, The Probabilistic Method, Academic Press, New York, 1992.

    MATH  Google Scholar 

  2. J. Baumgartner, F. Galvin, R. Laver and R. McKenzie. Game theoretic versions of partition relations, in: Colloq. Math. Soc. Jdnos Bolyai “Infinite and Finite sets” Keszthely, Hungary, 1973, 131–135.

    Google Scholar 

  3. J. Beck, On positional games, Journal of Combinatorial Theory, ser. A 30(1981), 117–133.

    Article  MATH  Google Scholar 

  4. J. Beck, Van der Waerden and Ramsey type games. Combinatorica 2(1981), 103–116.

    Article  Google Scholar 

  5. J. Beck, Remarks on positional games—Part I, Acta Math. Acad. Set Hungariea (1–2) 40(1982), 65–71.

    Article  Google Scholar 

  6. J. Beck, There is no fast method for finding monochromatic complete subgraphs, Journal of Combinatorial Theory, ser. B 34(1983), 58–64.

    Article  MATH  Google Scholar 

  7. J. Beck, Random graphs and positional games on the complete graph, Annals of Discrete Math. 28(1985), 7–13.

    Google Scholar 

  8. J. Beck, An algorithmic approach to the Lovász Local Lemma. I., Random Structures and Algorithms 2(1991), 343–365.

    Article  MathSciNet  MATH  Google Scholar 

  9. J. Beck, Parallel matching complexity of Ramsey’s theorem, manuscript (1992).

    Google Scholar 

  10. J. Beck, Deterministic graph games and a probabilistic intuition, manuscript (1993).

    Google Scholar 

  11. J. Beck and L. Csirmaz, Variations on a game, Journal of Combinatorial Theory, ser. A 33(1982), 297–315.

    Article  MathSciNet  MATH  Google Scholar 

  12. C. Berge, Sur les jeux positionelles, Cahiers Centre Études Reeh. Opér. 18(1976).

    Google Scholar 

  13. E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, London, 1982.

    MATH  Google Scholar 

  14. B. Bollobás, Random Graphs, Academic Press, London, 1985.

    MATH  Google Scholar 

  15. V. Chvátal and P. Erdős, Biased positional games, Annals of Discrete Math. 2(1978), 221–228.

    Article  MATH  Google Scholar 

  16. V. Chvátal, V. Rödl, E. Szemerédi and W. T. Trotter, The Ramsey number of a graph with bounded maximum degree, Journal of Combinatorial Theory, series B 34(1983), 239–243.

    Article  MathSciNet  MATH  Google Scholar 

  17. P. Erdős, Some remarks on the theory of graphs, Bull. Amer. Math. Soc. 53(1947), 292–294.

    Article  Google Scholar 

  18. P. Erdős, On a combinatorial problem, I, Nordisk. Mat. Tidskr. 11(1963), 5–10.

    MathSciNet  Google Scholar 

  19. P. Erdős and L. Lovász, Problems and results on 3-chromatic hypergraphs and some related questions, in: Infinite and Finite Sets (eds.: A. Hajn I et al.), Colloq. Math. Soc. J. Bolyai, 11, North-Holland, Amsterdam, 1975, 609–627.

    Google Scholar 

  20. P. Erdős and J. Selfridge, J, On a combinatorial game, Journal of Combinatorial Theory, ser. A 14(1973), 298–301.

    Article  Google Scholar 

  21. A. W. Hales and R. I. Jewett, On regularity and positional games, Trans. Amer. Math. Soc. 106(1963), 222–229.

    Article  MathSciNet  Google Scholar 

  22. J. Komlós and E. Szemerédi, Hamilton cycles in random graphs, in: Proc. of the Combinatorial Colloquium in Keszthely, Hungary, 1973, 1003–1010.

    Google Scholar 

  23. A. Lehman, A solution to the Shannon switching game, SIAM Journ. Appl. Math. 12(1964), 687–725.

    Article  MathSciNet  MATH  Google Scholar 

  24. L. Lovász, Combinatorial Problems and Exercises, North-Holland and Akademia Kiadó, 1979.

    Google Scholar 

  25. C. St. J. A. Nash-Williams, Edge-disjoint spanning trees of finite graphs, Journ. London Math. Soc. 36(1961), 445–450.

    Article  MATH  Google Scholar 

  26. L. Pòsa, Hamilton circuits in random graphs, Discrete Math. 14(1976), 359–364.

    Article  MathSciNet  MATH  Google Scholar 

  27. L. A. Székely, On two concepts of discrepancy in a class of combinatorial games, in: Colloq. Math. Soc. Jdnos Bolyai 37 “Finite and Infinite Sets” Eger, Hungary, 1981, North-Holland, 679–683.

    Google Scholar 

  28. W. T. Tutte, On the problem of decomposing a graph into n connected factors, Journ. London Math. Soc. 36(1961), 221–230.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Rutgers University, 08903, New Brunswick, New Jersey, USA

    József Beck

Authors
  1. József Beck
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. AT&T Bell Laboratories, 600 Mountain Avenue, NJ 07974, Murray Hill, USA

    Ronald L. Graham

  2. Department of Applied Mathematics, Charles University, Malostranske nam. 25, 11800, Praha, Czech Republic

    Jaroslav Nešetřil

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Beck, J. (1997). Games, Randomness and Algorithms. In: Graham, R.L., Nešetřil, J. (eds) The Mathematics of Paul Erdös I. Algorithms and Combinatorics, vol 13. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60408-9_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-60408-9_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-64394-1

  • Online ISBN: 978-3-642-60408-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation