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arXiv · 2602.18316

Ramsey theory of low-degree semialgebraic relations

Azem Adibelli·István Tomon
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Abstract

We prove that hypergraphs defined by low-degree polynomial inequalities contain large homogeneous subsets. Formally, let $H$ be an $r$-uniform hypergraph on $N$ vertices that is semialgebraic of constant description complexity, and each defining polynomial has degree at most $D$. Then $H$ contains a clique or an independent set of size $n$, where $N\leq \mbox{tw}_{3D^3}(n)$.

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Azem Adibelli, István Tomon. 2026-02-20. Ramsey theory of low-degree semialgebraic relations. https://arxiv.org/abs/2602.18316

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