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Rainbow-free 3-colorings of Abelian Groups

A 3-coloring of the elements of an abelian group is said to be rainbow--free if there is no 3-term arithmetic progression with its members having pairwise distinct colors. We give a structural characterization of rainbow--free colorings of abelian groups. This characterization proves a conjecture of Jungić et al. on the size of the smallest chromatic class of a rainbow-free 3-coloring of cyclic groups.

preprint2011arXivOpen access
Amanda MontejanoOriol Serra
math.CO
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Amanda MontejanoOriol Serra

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