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This research explores the chromatic number of the plane and its relationship with De Grey's 1581-vertex unit-distance graph.

August 13, 2026Open Access

De Grey's 1581-Vertex Graph and the Golden Ratio in the Chromatic Number of the Plane — E8 Intelligence Research

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Finding connections between unit-distance graphs and the chromatic number of the plane, implying deep geometric links.

This research explores the chromatic number of the plane and its relationship with De Grey's 1581-vertex unit-distance graph.
Analyzed bounds of the chromatic number χ(R²) for coloring a plane with points 1 unit apart.
Investigated the geometric properties of unit-distance graphs using hexagonal lattice symmetries.
Confirmed lower bound of the chromatic number at 5 through De Grey's 1581-vertex graph.
Explored the presence of the golden ratio in some unit-distance graph constructions.

Andrew Stewart Caldin (2026) studied this question.

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