Lower bounds for Ramsey numbers of bounded degree hypergraphs
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913992781332480 |
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| author | Bradač, Domagoj Hunter, Zach Sudakov, Benny |
| author_facet | Bradač, Domagoj Hunter, Zach Sudakov, Benny |
| contents | We prove that, for all $k \ge 3,$ and any integers $Δ, n$ with $n \ge Δ,$ there exists a $k$-uniform hypergraph on $n$ vertices with maximum degree at most $Δ$ whose $4$-color Ramsey number is at least $\mathrm{tw}_k(c_k Δ) \cdot n$, for some constant $c_k > 0$, where $\mathrm{tw}_k$ denotes the tower function. For $k \ge 4,$ this is tight up to the constant $c_k$ and for $k = 3$ it is known to be tight up to a factor of $\log Δ$ on top of the tower. It extends a well-known result of Graham, Rödl and Ruciński for graphs and answers a question of Conlon, Fox and Sudakov from 2008. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_20863 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lower bounds for Ramsey numbers of bounded degree hypergraphs Bradač, Domagoj Hunter, Zach Sudakov, Benny Combinatorics We prove that, for all $k \ge 3,$ and any integers $Δ, n$ with $n \ge Δ,$ there exists a $k$-uniform hypergraph on $n$ vertices with maximum degree at most $Δ$ whose $4$-color Ramsey number is at least $\mathrm{tw}_k(c_k Δ) \cdot n$, for some constant $c_k > 0$, where $\mathrm{tw}_k$ denotes the tower function. For $k \ge 4,$ this is tight up to the constant $c_k$ and for $k = 3$ it is known to be tight up to a factor of $\log Δ$ on top of the tower. It extends a well-known result of Graham, Rödl and Ruciński for graphs and answers a question of Conlon, Fox and Sudakov from 2008. |
| title | Lower bounds for Ramsey numbers of bounded degree hypergraphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2502.20863 |