The chromatic number of the plane is at least 5 - a new proof

2018/05/01 by Geoffrey Exoo, Exoo, Geoffrey, Dan Ismailescu +1 · 1 citation
Computer Science · Engineering · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Mathematics and Applications #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1805.00157

openalex publication_date 2018/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Cited by

• Ramsey problems for graphs in Euclidean spaces and Cartesian powers

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• A 5-chromatic same-distance graph in the hyperbolic plane
• A 6-chromatic two-distance graph in the plane
• The chromatic number of the plane with an interval of forbidden distances is at least 7
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• Odd distances in colourings of the plane