Geodesic
Rainbow-free 3-colorings of abelian groups
The electronic journal of combinatorics, Tome 19 (2012) no. 1
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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.
DOI : 10.37236/2054
Classification : 05D10, 11B75, 11P70
Mots-clés : smallest chromatic class of a rainbow-free 3-coloring of cyclic groups 
@article{10_37236_2054,
     author = {Amanda Montejano and Oriol Serra},
     title = {Rainbow-free 3-colorings of abelian groups},
     journal = {The electronic journal of combinatorics},
     year = {2012},
     volume = {19},
     number = {1},
     doi = {10.37236/2054},
     zbl = {1243.05239},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/2054/}
}
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Amanda Montejano; Oriol Serra. Rainbow-free 3-colorings of abelian groups. The electronic journal of combinatorics, Tome 19 (2012) no. 1. doi: 10.37236/2054

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