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Density theorems and extremal hypergraph problems

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Abstract

We present alternative proofs of density versions of some combinatorial partition theorems originally obtained by E. Szemerédi, H. Furstenberg and Y. Katznelson. These proofs are based on an extremal hypergraph result which was recently obtained independently by W. T. Gowers and B. Nagle, V. Rödl, M. Schacht, J. Skokan by extending Szemerédi’s regularity lemma to hypergraphs.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Emory University, 30322, Atlanta, GA, USA

    V. Rödl & E. Tengan

  2. Institut für Informatik, Humboldt Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany

    M. Schacht

  3. College of Education, Ryukyu University, Nishihara, 903-0213, Okinawa, Japan

    N. Tokushige

Authors
  1. V. Rödl
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  2. E. Tengan
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  3. M. Schacht
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  4. N. Tokushige
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Corresponding author

Correspondence to V. Rödl.

Additional information

Research was partially supported by NSF Grant DMS 0300529.

Research was partially supported by the Deutsche Forschungsgemeinschaft within the European graduate program ‘Combinatorics, Geometry, and Computation’ (No. GRK 588/2) and by grant SCHA 1263/1-1.

Research was supported by a scholarship from CAPES, Brazil.

Research was supported by MEXT Grant-in-Aid for Scientific Research (B) 16340027.

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Rödl, V., Tengan, E., Schacht, M. et al. Density theorems and extremal hypergraph problems. Isr. J. Math. 152, 371–380 (2006). https://doi.org/10.1007/BF02771992

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  • DOI: https://doi.org/10.1007/BF02771992

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