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arXiv · 2609.00583

A 21-Coloring of the Plane Without Monochromatic Unit-Area Rectangles

Gary Hu·Yumo Liu
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Abstract

Erdős and Graham asked whether every finite coloring of the plane must contain a monochromatic rectangle of any prescribed area. Kovač gave a negative answer by constructing a $25$-coloring with no monochromatic rectangle of area $1$. We reduce the number of colors to $21$ by replacing the square cells in his construction with regular hexagons.

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Gary Hu, Yumo Liu. 2026-09-01. A 21-Coloring of the Plane Without Monochromatic Unit-Area Rectangles. https://arxiv.org/abs/2609.00583

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