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arXiv · 2507.23623

Ramsey numbers for 1-degenerate 3-graphs

Peter Allen·Simona Boyadzhiyska·Matías Pavez-Signé
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Abstract

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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Peter Allen, Simona Boyadzhiyska, Matías Pavez-Signé. 2026-05-29. Ramsey numbers for 1-degenerate 3-graphs. https://arxiv.org/abs/2507.23623

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