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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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