A 21-Coloring of the Plane Without Monochromatic Unit-Area Rectangles
Gary Hu, Yumo Liu
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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