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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5 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

508.lean

Retained formal statement2 of 5

Aubrey de Grey improved the lower bound for the chromatic number of the plane to 5 in 2018 using a graph that has >1000 nodes.

"The chromatic number of the plane is at least 5" Aubrey D. N. J. de Grey, 2018 (https://doi.org/10.48550/arXiv.1804.02385)

FormalConjectures/ErdosProblems/508.leanErdos508.HadwigerNelsonAtLeastFive1 lineExact file

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

SolvedStatement only, no proof

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