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arXiv · 2010.12668

What percent of the plane can be properly 5- and 6-colored?

Jaan Parts
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Abstract

We present a tiling of more than 99.985698% of the Euclidean plane with six colors, reducing the previous record for uncovered fraction of the plane by about 12.8%. We also present a tiling of more than 95.99% of the plane with five colors. It is thus shown that any unit-distance graph of order at most 6992 and 24 in the plane can be properly 6-colored and 5-colored, respectively.

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Jaan Parts. 2020-10-23. What percent of the plane can be properly 5- and 6-colored?. https://arxiv.org/abs/2010.12668

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