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Amanda Montejano
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Oriol Serra
Abstract
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.