Skip to main content
SpringerLink
Log in

On ramsey families of sets

  • Original Papers
  • Published:
Graphs and Combinatorics Aims and scope Submit manuscript

Abstract

The main result of this paper is a lemma which can be used to prove the existence of highchromatic subhypergraphs of large girth in various hypergraphs. In the last part of the paper we use amalgamation techniques to prove the existence for everyl, k ≥ 3 of a setA of integers such that the hypergraph having as edges all the arithmetic progressions of lengthk inA has both chromatic number and girth greater thanl.

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. Erdös, P., Hajnal, A.: On chromatic number of graphs and set-systems. Acta Math. Acad. Sci. Hung.17, 61–99 (1966)

    Google Scholar 

  2. Erdös, P., Rado, R.: A combinatorial theorem, J. London Math. Soc.25, 249–255 (1950)

    Google Scholar 

  3. Graham, R.L., Nešetřil, J.: Large minimal sets which force long arithmetic progressions. J. Comb. Theory (A)42, 270–276 (1986)

    Google Scholar 

  4. Graham, R.L., Rothschild, B.L., Spencer, J.H.: Ramsey Theory. New York: John Wiley & Sons 1980

    Google Scholar 

  5. Hales, A.W., Jewett, R.I.: Regularity and positional games. Trans. Amer. Math. Soc.106, 222–229 (1963)

    Google Scholar 

  6. Nešetřil, J., Rödl, V.: Partition (Ramsey) theory—A survey. Colloq. Math. Soc. Janos Bolyai.18, 759–792 (1976)

    Google Scholar 

  7. Prömmel, H.J., Rödl, V.: An elementary proof of the canonizing version of Galai-Witt's theorem. J. Comb. Theory (A)42, 144–149 (1986)

    Google Scholar 

  8. Prömmel, H.J., Rothschild, B.L.: Restricted Gallai Witt theorem. (to appear)

  9. Spencer, J.: Restricted Ramsey configurations. J. Comb. Theory (A)19, 278–286 (1975)

    Google Scholar 

  10. Szemerédi: On sets of integers containing nok elements in arithmetic progression. Acta Arith.27, 199–245 (1975)

    Google Scholar 

  11. van der Waerden, B.L.: Beweis einer Baudetschen Vermutung. Nieuw Arch. Wisk.15, 212–216 (1927)

    Google Scholar 

  12. Nešetřil, J., Rödl, V.: Sparse Ramsey graphs. Combinatorica4, 71–78 (1984)

    Google Scholar 

  13. Ramsey, F.P.: On a problem of formal logic, Proc. London Math. Soc.30, 264–286 (1930)

    Google Scholar 

  14. Erdös, P., Rado, R.: Combinatorial theorems on classifications of subsets of a given set. Proc. London Math. Soc.2, 417–439 (1952)

    Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Vojtěch Rödl

  2. Emory University, 30322, Atlanta, GA, USA

    Vojtěch Rödl

Authors
  1. Vojtěch Rödl
    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

Rödl, V. On ramsey families of sets. Graphs and Combinatorics 6, 187–195 (1990). https://doi.org/10.1007/BF01787730

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01787730

Keywords

Search

Navigation