Ramsey numbers for 1-degenerate 3-graphs
Abstract
We construct a 3-uniform 1-degenerate hypergraph on n vertices whose 2-colour Ramsey number is Ω(n3/2/ 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(n3/2).
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