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The chromatic number of the plane is at least 5

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arxiv 1804.02385 v3 pith:E5PEK6SY submitted 2018-04-08 math.CO

Aubrey D.N.J. de Grey This is my paper · ORCID
classification math.CO
keywords planeboundchromaticcolourablediscoveredfamilyfinitegraph
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We present a family of finite unit-distance graphs in the plane that are not 4-colourable, thereby improving the lower bound of the Hadwiger-Nelson problem. The smallest such graph that we have so far discovered has 1581 vertices.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A unit-distance graph in the plane with independence ratio below 1/4

    math.CO 2026-06 unverdicted novelty 7.0 of 10

    Existence of a unit-distance graph with independence ratio strictly below 1/4 is established via a two-vertex augmentation of a prior 27-vertex construction, disproving a conjecture on geometric fractional chromatic number.

  2. On lower bounds of the density of planar periodic sets without unit distances

    math.MG 2024-11 conditional novelty 6.0 of 10

    A new maximal-independent-set formulation for periodic unit-distance-free sets in the plane is tested and shown, in the parameter range tried, not to beat Croft's 1967 density lower bound of 0.22936.

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