When are off-diagonal hypergraph Ramsey numbers polynomial?
Fuente:
arXiv
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| Autori principali: | , , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
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| _version_ | 1866912674422456320 |
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| author | Conlon, David Fox, Jacob Gunby, Benjamin He, Xiaoyu Mubayi, Dhruv Suk, Andrew Verstraëte, Jacques Yu, Hung-Hsun Hans |
| author_facet | Conlon, David Fox, Jacob Gunby, Benjamin He, Xiaoyu Mubayi, Dhruv Suk, Andrew Verstraëte, Jacques Yu, Hung-Hsun Hans |
| contents | A natural open problem in Ramsey theory is to determine those $3$-graphs $H$ for which the off-diagonal Ramsey number $r(H, K_n^{(3)})$ grows polynomially with $n$. We make substantial progress on this question by showing that if $H$ is tightly connected or has at most two tight components, then $r(H, K_n^{(3)})$ grows polynomially if and only if $H$ is contained in an iterated blowup of an edge. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_13812 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | When are off-diagonal hypergraph Ramsey numbers polynomial? Conlon, David Fox, Jacob Gunby, Benjamin He, Xiaoyu Mubayi, Dhruv Suk, Andrew Verstraëte, Jacques Yu, Hung-Hsun Hans Combinatorics 05D10 (Primary), 05D40 (Secondary) A natural open problem in Ramsey theory is to determine those $3$-graphs $H$ for which the off-diagonal Ramsey number $r(H, K_n^{(3)})$ grows polynomially with $n$. We make substantial progress on this question by showing that if $H$ is tightly connected or has at most two tight components, then $r(H, K_n^{(3)})$ grows polynomially if and only if $H$ is contained in an iterated blowup of an edge. |
| title | When are off-diagonal hypergraph Ramsey numbers polynomial? |
| topic | Combinatorics 05D10 (Primary), 05D40 (Secondary) |
| url | https://arxiv.org/abs/2411.13812 |