Rainbow-free $3$-colorings of Abelian Groups

Amanda Montejano, Oriol Serra


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.

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