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arXiv · 2206.12630

On upper bounds for the multi-fold chromatic numbers of the plane

Jaan Parts
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Abstract

The multi-fold chromatic number of the plane $χ_m$ is the smallest number of colors $k$, sufficient to color each point of the Euclidean plane in exactly $m$ colors, so that for any pair of points at a unit distance from each other, two corresponding $m$-subsets of $k$-set do not contain any common color. We consider upper bounds for $m$-fold chromatic numbers of the plane. Our main result is that for any $m$ the inequality $χ_m<(1+2/\sqrt3)^2\cdot m+3.501$ holds.

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Jaan Parts. 2022-06-25. On upper bounds for the multi-fold chromatic numbers of the plane. https://arxiv.org/abs/2206.12630

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