Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rainbow-free 3-colorings of Abelian Groups   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.

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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: cs
29
The categories of this paper are: funct-an