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

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Abstract

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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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Indiana State University, Terre Haute, IN, 47809, USA

    Geoffrey Exoo

  2. Mathematics Department, Hofstra University, Hempstead, NY, 11549, USA

    Dan Ismailescu

Authors
  1. Geoffrey Exoo
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  2. Dan Ismailescu
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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). https://doi.org/10.1007/s00454-019-00058-1

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  • DOI: https://doi.org/10.1007/s00454-019-00058-1

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