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arXiv · 2609.18995

Bounded VC-dimension implies the Erdős--Rado sunflower conjecture

Gennian Ge·Jian Wang·Zixiang Xu·Xiaochen Zhao
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Abstract

The Erdős--Rado sunflower conjecture asserts that, for every fixed integer $r\ge 3$, there is a constant $K(r)$ such that every $\ell$-uniform family with more than $K(r)^{\ell}$ members contains an $r$-sunflower. We prove this conjecture for families of bounded VC-dimension.

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Gennian Ge, Jian Wang, Zixiang Xu, Xiaochen Zhao. 2026-07-17. Bounded VC-dimension implies the Erdős--Rado sunflower conjecture. https://arxiv.org/abs/2609.18995

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