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Monochromatic Translates of Configurations in the Plane

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Abstract

It is shown that every red–blue coloring of the plane, without two blue points distance 1 apart, must have a red translate of every three-point configuration. A seven-point configuration S and a red–blue coloring are exhibited, which avoids both distance one in blue and translates of S in red.

Keywords

Euclidean Ramsey
translates

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