Rainbow-free 3-colorings of Abelian Groups
Combinatorics
2011-04-04 v1
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 Jungi\'c et al. on the size of the smallest chromatic class of a rainbow-free 3-coloring of cyclic groups.
Keywords
Cite
@article{arxiv.1104.0194,
title = {Rainbow-free 3-colorings of Abelian Groups},
author = {Amanda Montejano and Oriol Serra},
journal= {arXiv preprint arXiv:1104.0194},
year = {2011}
}
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19 pages