English

Ramsey numbers for 1-degenerate 3-graphs

Combinatorics 2025-08-01 v1

Abstract

We construct a 3-uniform 1-degenerate hypergraph on nn vertices whose 2-colour Ramsey number is Ω(n3/2/logn)\Omega\big(n^{3/2}/\log n\big). This shows that all remaining open cases of the hypergraph Burr-Erd\H{o}s conjecture are false. Our graph is a variant of the celebrated hedgehog graph. We additionally show near-sharp upper bounds, proving that all 3-uniform generalised hedgehogs have 2-colour Ramsey number O(n3/2)O\big(n^{3/2}\big).

Keywords

Cite

@article{arxiv.2507.23623,
  title  = {Ramsey numbers for 1-degenerate 3-graphs},
  author = {Peter Allen and Simona Boyadzhiyska and Matías Pavez-Signé},
  journal= {arXiv preprint arXiv:2507.23623},
  year   = {2025}
}

Comments

5 pages, 2 figures

R2 v1 2026-07-01T04:27:59.765Z