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arXiv · 2607.11782

All simplices exhibit canonical Ramsey property

Gennian Ge·Yang Shu·Zixiang Xu·Wenjun Yu
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Abstract

We prove that all nondegenerate simplices have the canonical Ramsey property, thereby resolving a central open problem in canonical Euclidean Ramsey theory and providing a canonical counterpart to the celebrated simplex Ramsey theorem of Frankl and Rödl~[JAMS, 1990].

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Gennian Ge, Yang Shu, Zixiang Xu, Wenjun Yu. 2026-07-13. All simplices exhibit canonical Ramsey property. https://arxiv.org/abs/2607.11782

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