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Bounded VC-dimension implies the Erd\H{o}s--Rado sunflower conjecture

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Gennian Ge, Jian Wang, Zixiang Xu, Xiaochen Zhao

Combinatorics · Submitted 17 Jul 2026

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We prove this conjecture for families of bounded VC-dimension.

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arXiv ID2609.18995 (version 1)
Pith IDJ2DAKSKE, Pith's permanent record of this paper and its review
CitationGennian Ge, Jian Wang, Xiaochen Zhao, Zixiang Xu. "Bounded VC-dimension implies the Erd\H{o}s--Rado sunflower conjecture." arXiv:2609.18995 (2026). https://pith.science/paper/J2DAKSKE
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,342 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.81 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.43 · compares with prior results 0.11 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

The Erd\H{o}s--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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#sentencerolethe authors' own workstates the main conclusionstrength
s0 The Erd\H{o}s--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. background 1.00 0.03 0.04 asserted 0.62
s1 We prove this conjecture for families of bounded VC-dimension. result 0.58 0.97 0.96 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

The Erd\H{o}s--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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