Ramsey theory of low-degree semialgebraic relations

Fuente: arXiv
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Main Authors: Adibelli, Azem, Tomon, István
Format: Preprint
Published: 2026
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author Adibelli, Azem
Tomon, István
author_facet Adibelli, Azem
Tomon, István
contents 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 $N\leq \mbox{tw}_{3D^3}(n)$.
format Preprint
id arxiv_https___arxiv_org_abs_2602_18316
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Ramsey theory of low-degree semialgebraic relations
Adibelli, Azem
Tomon, István
Combinatorics
Logic
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 $N\leq \mbox{tw}_{3D^3}(n)$.
title Ramsey theory of low-degree semialgebraic relations
topic Combinatorics
Logic
url https://arxiv.org/abs/2602.18316