Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 40 min ago
PreprintCC BY 4.0arXiv

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

  • Gennian Ge
  • Jian Wang
  • Zixiang Xu
  • Xiaochen Zhao
Open at sourcePDFDOICite

Abstract

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

Related

  1. Proof of the Erdős-Szemerédi sunflower conjecture
    Matija Bucić, Fankang He, Hyunwoo Lee
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv
  2. Linear dependencies, polynomial factors in the Duke–Erdős forbidden sunflower problem – CORRIGENDUM
    Andrey Kupavskii, Fedor Noskov
    Forum of Mathematics, SigmaPeer-reviewedCC BY 4.0General mathematicsCrossref
  3. The Erdős similarity problem for null sequences with adjacent ratios bounded below
    Kan Jiang, Lifeng Xi
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  4. Towards the Erdős matching conjecture for 4‐uniform hypergraphs: Stability and applications
    Péter Frankl, Hongliang Lu, Jie Ma +1
    MathematikaPeer-reviewedLicence not statedFull text11 citedCombinatorics & discrete mathematicsOpenAlex
  5. The Erdős--Chvátal Simplex Conjecture
    Jing Huang
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{ge2026bounded,
  title = {{Bounded VC-dimension implies the Erdős--Rado sunflower conjecture}},
  author = {Gennian Ge and Jian Wang and Zixiang Xu and Xiaochen Zhao},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.18995},
  eprint = {2609.18995},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.18995},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Bounded VC-dimension implies the Erdős--Rado sunflower conjecture
AU  - Gennian Ge
AU  - Jian Wang
AU  - Zixiang Xu
AU  - Xiaochen Zhao
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.18995
UR  - https://arxiv.org/abs/2609.18995
AB  - The Erdős--Rado sunflower conjecture asserts that, for every fixed integer r≥ 3, there is a constant K(r) such that every ℓ-uniform family with more than K(r)^ℓ members contains an r-sunflower. We prove this conjecture for families of bounded VC-dimension.
ER  -