Ramsey Numbers for 1-Degenerate 3-Graphs - Allen, Peter; Boyadzhiyska, Simona; Pavez-Signé, Matías (The Electronic Journal of Combinatorics, 2026)
We construct a 3-uniform 1-degenerate hypergraph on n vertices whose 2-colour Ramsey number is Ω(n^3/2/n). 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(n^3/2).