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arXiv · 1502.04413

The structure of rainbow-free colorings for linear equations on three variables in Zp

Mario Huicochea·Amanda Montejano
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Abstract

Let p be a prime number and Zp be the cyclic group of order p. A coloring of Zp is called rainbow-free with respect to a certain equation, if it contains no rainbow solution of the same, that is, a solution whose elements have pairwise distinct colors. In this paper we describe the structure of rainbow-free 3-colorings of Zp with respect to all linear equations on three variables. Consequently, we determine those linear equations on three variables for which every 3-coloring (with nonempty color classes) of Zp contains a rainbow solution of it.

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Mario Huicochea, Amanda Montejano. 2015-02-16. The structure of rainbow-free colorings for linear equations on three variables in Zp. https://arxiv.org/abs/1502.04413

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