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arXiv · 1804.02385

The chromatic number of the plane is at least 5

Aubrey D. N. J. de Grey
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Abstract

We present a family of finite unit-distance graphs in the plane that are not 4-colourable, thereby improving the lower bound of the Hadwiger-Nelson problem. The smallest such graph that we have so far discovered has 1581 vertices.

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Aubrey D. N. J. de Grey. 2018-05-30. The chromatic number of the plane is at least 5. https://arxiv.org/abs/1804.02385

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