On tight tree-complete hypergraph Ramsey numbers
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916543603933184 |
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| author | Nie, Jiaxi |
| author_facet | Nie, Jiaxi |
| contents | Chvátal showed that for any tree $T$ with $k$ edges the Ramsey number $R(T,n)=k(n-1)+1$ ("Tree-complete graph Ramsey numbers." Journal of Graph Theory 1.1 (1977): 93-93). For $r=3$ or $4$, we show that, if $T$ is an $r$-uniform non-trivial tight tree, then the hypergraph Ramsey number $R(T,n)=Θ(n^{r-1})$. The 3-uniform result comes from observing a construction of Cooper and Mubayi. The main contribution of this paper is the 4-uniform construction, which is inspired by the Cooper-Mubayi 3-uniform construction. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_19461 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On tight tree-complete hypergraph Ramsey numbers Nie, Jiaxi Combinatorics 05C65, O5D10 Chvátal showed that for any tree $T$ with $k$ edges the Ramsey number $R(T,n)=k(n-1)+1$ ("Tree-complete graph Ramsey numbers." Journal of Graph Theory 1.1 (1977): 93-93). For $r=3$ or $4$, we show that, if $T$ is an $r$-uniform non-trivial tight tree, then the hypergraph Ramsey number $R(T,n)=Θ(n^{r-1})$. The 3-uniform result comes from observing a construction of Cooper and Mubayi. The main contribution of this paper is the 4-uniform construction, which is inspired by the Cooper-Mubayi 3-uniform construction. |
| title | On tight tree-complete hypergraph Ramsey numbers |
| topic | Combinatorics 05C65, O5D10 |
| url | https://arxiv.org/abs/2412.19461 |