The structure of rainbow-free colorings for linear equations on three variables in Zp
Combinatorics
2015-02-17 v1
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.
Cite
@article{arxiv.1502.04413,
title = {The structure of rainbow-free colorings for linear equations on three variables in Zp},
author = {Mario Huicochea and Amanda Montejano},
journal= {arXiv preprint arXiv:1502.04413},
year = {2015}
}