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The Chromatic Number of the Plane is At Least 5: A New Proof


We present an alternate proof of the fact that given any 4-coloring of the plane there exist two points one unit apart which are identically colored.

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Correspondence to Dan Ismailescu.

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Supported by Grant No. 1751765 from the National Science Foundation, USA.

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Exoo, G., Ismailescu, D. The Chromatic Number of the Plane is At Least 5: A New Proof. Discrete Comput Geom 64, 216–226 (2020).

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  • Chromatic number of the plane
  • Hadwiger–Nelson problem
  • Unit distance graphs