PreprintarXiv licencearXiv
A note on the Kővári--Sós--Turán theorem for stable hypergraphs
Abstract
In this note, we prove a stronger version of the Kővári-Sós-Turán theorem for partition-wise k-stable r-hypergraphs. More precisely, we show that for every k,r∈ℕ≥ 2 there is η=η(r,k)>0 such that if H=(V;E) is a partition-wise k-stable r-uniform K(r)t,…,t-free hypergraph with |V|=n, then |E| = Or,k,t(nr−η). Crucially, η is independent of t. The proof follows the pseudofinite regime used by Chernikov and Starchenko to prove an analogous version of Erdős-Hajnal for stable hypergraphs.
Related
- A note on functional non-central limit theorem for periodic regime-switching stable-like processes
- Weighted Turán densities for hypergraphs
- The ℓ-degree Turán densities of hypergraphs: infinite families and their finite subfamilies
- Rational values and non-principality for ℓ-degree Turán densities of hypergraphs
- The Turán number of Berge paths in connected hypergraphs
BibTeX
@misc{papadopoulos2026note,
title = {{A note on the Kővári--Sós--Turán theorem for stable hypergraphs}},
author = {Aris Papadopoulos},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06684},
eprint = {2610.06684},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06684},
}
RIS
TY - UNPB
TI - A note on the Kővári--Sós--Turán theorem for stable hypergraphs
AU - Aris Papadopoulos
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06684
UR - https://arxiv.org/abs/2610.06684
AB - In this note, we prove a stronger version of the Kővári-Sós-Turán theorem for partition-wise k-stable r-hypergraphs. More precisely, we show that for every k,r∈ℕ_≥ 2 there is η=η(r,k)>0 such that if H=(V;E) is a partition-wise k-stable r-uniform K^(r)_t,…,t-free hypergraph with |V|=n, then |E| = O_r,k,t(n^r−η). Crucially, η is independent of t. The proof follows the pseudofinite regime used by Chernikov and Starchenko to prove an analogous version of Erdős-Hajnal for stable hypergraphs.
ER -