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arXiv · 2606.12325

A note on geometric colorings of the Moser lattice

Ákos Dúcz
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Abstract

In arXiv:2311.10069, Matolcsi et al. show that the fractional chromatic number of the plane is at least 4. Their proof uses a 27-vertex unit-distance graph in the Moser lattice, with geometric fractional chromatic number exactly 4. We show that this bound is tight for graphs in the Moser lattice by exhibiting geometric 4-colorings of the entire lattice. The same colorings also extend to the entire Moser ring.

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Ákos Dúcz. 2026-06-10. A note on geometric colorings of the Moser lattice. https://arxiv.org/abs/2606.12325

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