Euclidean Gallai-Ramsey Theory
Combinatorics
2022-09-28 v1
Abstract
In this paper, we introduce Euclidean Gallai-Ramsey theory, by combining Euclidean Ramsey theory and Gallai-Ramsey theory on graphs. More precisely, we consider the following problem: For an integer and configurations and , does there exist an integer such that for any -coloring of the points of -dimensional Euclidean space with , there is a monochromatic configuration congruent to or a rainbow configuration congruent to ? In particular, we give a bound on for some configurations and , such as triangles and rectangles. Those are extensions of ordinary Euclidean Ramsey theory where the purpose is to find a monochromatic configuration.
Cite
@article{arxiv.2209.13247,
title = {Euclidean Gallai-Ramsey Theory},
author = {Yaping Mao and Kenta Oeki and Zhao Wang},
journal= {arXiv preprint arXiv:2209.13247},
year = {2022}
}