Ramsey numbers for 1-degenerate 3-graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917547898568704 |
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| author | Allen, Peter Boyadzhiyska, Simona Pavez-Signé, Matías |
| author_facet | Allen, Peter Boyadzhiyska, Simona Pavez-Signé, Matías |
| contents | 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 $O\big(n^{3/2}\big)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23623 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ramsey numbers for 1-degenerate 3-graphs Allen, Peter Boyadzhiyska, Simona Pavez-Signé, Matías Combinatorics 05D10 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 $O\big(n^{3/2}\big)$. |
| title | Ramsey numbers for 1-degenerate 3-graphs |
| topic | Combinatorics 05D10 |
| url | https://arxiv.org/abs/2507.23623 |