Ramsey lower bounds for bounded degree hypergraphs
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866912982710091776 |
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| author | Fan, Chunchao Lin, Qizhong |
| author_facet | Fan, Chunchao Lin, Qizhong |
| contents | We prove that for all $k \ge 3$ and any integers $Δ, n$ with $n \ge 2^Δ,$ there exists a $k$-graph on $n$ vertices with maximum degree at most $Δ$ such that $r(H)\geq\tw_{k-1}(c_k Δ) \cdot n$ for some constant $c_k > 0$, where $\tw_k$ denotes the tower function. This makes the first progress toward a problem proposed by Conlon, Fox, and Sudakov (2009), who asked whether $r(H)\geq\tw_{k}(c_k Δ) \cdot n$ holds. Our proof relies on a novel construction of a $k$-graph on a growing number of vertices $n$ while keeping the maximum degree bounded by a fixed $Δ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24627 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ramsey lower bounds for bounded degree hypergraphs Fan, Chunchao Lin, Qizhong Combinatorics We prove that for all $k \ge 3$ and any integers $Δ, n$ with $n \ge 2^Δ,$ there exists a $k$-graph on $n$ vertices with maximum degree at most $Δ$ such that $r(H)\geq\tw_{k-1}(c_k Δ) \cdot n$ for some constant $c_k > 0$, where $\tw_k$ denotes the tower function. This makes the first progress toward a problem proposed by Conlon, Fox, and Sudakov (2009), who asked whether $r(H)\geq\tw_{k}(c_k Δ) \cdot n$ holds. Our proof relies on a novel construction of a $k$-graph on a growing number of vertices $n$ while keeping the maximum degree bounded by a fixed $Δ$. |
| title | Ramsey lower bounds for bounded degree hypergraphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2603.24627 |