Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.
Updated
Bounded VC-dimension implies the Erdos–Rado sunflower conjecture
Ge, Gennian, Jian Wang, Zixiang Xu, and Xiaochen Zhao, Bounded VC-dimension implies the Erdős–Rado sunflower conjecture, arXiv:2609.18995v1 (2026).
The abstract asserts the sunflower conjecture for uniform set families of bounded VC dimension. The bound is exponential in the uniformity for fixed sunflower size and VC dimension. The VC-dimension restriction remains a hypothesis, so the assertion does not settle the unrestricted catalog question.
The held PDF is this arXiv version, accompanied by its arXiv record, TeX source and HTML. The arXiv record, read 2026-10-15, names the Creative Commons Attribution 4.0 license.
Read status. The abstract and bibliographic record were read. The proof has not been checked here.
Source: https://arxiv.org/abs/2609.18995v1.
Bears on. Problem 20: the stated scope above supplies a related result or a limitation of a possible route.