Graphs and Combinatorics

, Volume 3, Issue 1, pp 145–158 | Cite as

Large independent sets in shift-invariant graphs

Solution of Bergelson's problem
  • Igor Kříž
Article

Abstract

We construct shift-invariant graphs with chromatic number ∞ and independent sets of density close to 1/2.

Keywords

Chromatic Number 

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References

  1. 1.
    Bergelson, V.: Open problem. Joint summer conference of AMS on Ramsey theory, Arcata, 1985Google Scholar
  2. 2.
    Kronecker, L.: Werke, Band 3. Halbband 1, Leipzig 1899Google Scholar
  3. 3.
    Lovász, L.: Kneser's conjecture, chromatic number and homotopy. J. Comb. Theory (A)25, 319–324 (1978)Google Scholar
  4. 4.
    Szemerédi, E.: On sets of integers containing nok elements in arithmetic progression. Acta Arith.27, 199–245 (1975)Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Igor Kříž
    • 1
  1. 1.Praha 4Czechoslovakia

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