A 3–coloring of an abelian group G is rainbow–free if there is no 3–term arithmetic
progression with its members having pairwise distinct colors. We describe
the structure of rainbow–free colorings of abelian groups. This structural description
proves a conjecture of Jungi´c et al. on the size of the smallest chromatic class of a rainbow–free coloring of cyclic groups.
Montejano, A.; Serra, O. Rainbow-free 3-colorings in abelian groups. "Electronic notes in discrete mathematics", 27 Juliol 2009, núm. 34, p. 133-137.