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Ramsey numbers for 1-degenerate 3-graphs
Peter Allen, Simona Boyadzhiyska, Matías Pavez-Signé · 2025-07-31 · via math updates on arXiv.org

We construct a 3-uniform 1-degenerate hypergraph on $n$ vertices whose 2-colour Ramsey number is $Ω\big(n^{3/2}/\log n\big)$. This shows that all remaining open cases of the hypergraph Burr-Erdős 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 $O\big(n^{3/2}\big)$.

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