Erdős problem 508 · problems.science

This upper bound for the chromatic number of the plane was observed by John R. Isbell. His approach was dividing the plane into hexagons of uniform size and coloring them with a repeating pattern. A proof can probably be found in:

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FormalConjectures/ErdosProblems/

508.lean

Retained formal statement3 of 5

The chromatic number of the plane is at least 3.

This is proven by considering an equilateral triangle in the plane.

FormalConjectures/ErdosProblems/508.leanErdos508.HadwigerNelsonAtLeastThree1 lineExact file

13 ≤ (SimpleGraph.UnitDistancePlaneGraph Set.univ).chromaticNumber

TextbookStatement only, no proof

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