Ramsey numbers for 1-degenerate 3-graphs
Combinatorics
2025-08-01 v1
Abstract
We construct a 3-uniform 1-degenerate hypergraph on vertices whose 2-colour Ramsey number is . 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 .
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