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On the Existence of Rainbow 4-Term Arithmetic Progressions

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Abstract

For infinitely many natural numbers n, we construct 4-colorings of [n]  =  {1, 2, ..., n}, with equinumerous color classes, that contain no 4-term arithmetic progression whose elements are colored in distinct colors. This result solves an open problem of Jungić et al. (Comb Probab Comput 12:599–620, 2003) Axenovich and Fon-der-Flaass (Electron J Comb 11:R1, 2004).

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Authors and Affiliations

  1. Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge, England

    David Conlon

  2. Department of Mathematics, Simon Fraser University, Burnaby, Canada

    Veselin Jungić

  3. Department of Mathematics, Rutgers University, Piscataway, NJ, 08854, USA

    Radoš Radoičić

  4. Baruch College, CUNY, New York, NY, 10010, USA

    Radoš Radoičić

Authors
  1. David Conlon
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  2. Veselin Jungić
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  3. Radoš Radoičić
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Correspondence to Radoš Radoičić.

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Conlon, D., Jungić, V. & Radoičić, R. On the Existence of Rainbow 4-Term Arithmetic Progressions. Graphs and Combinatorics 23, 249–254 (2007). https://doi.org/10.1007/s00373-007-0723-2

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  • DOI: https://doi.org/10.1007/s00373-007-0723-2

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