Ramsey theory of low-degree semialgebraic relations
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911459553837056 |
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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 |