Ramsey theory of low-degree semialgebraic relations
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 $N\leq \mbox{tw}_{3D^3}(n)$.
Fields of Study & Subjects
Limits and Structures in Graph Theory
Advanced Combinatorial Mathematics
Advanced Topology and Set Theory
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 20 February 2026
- Language
- EN
- Document type
- Preprint