The Ramsey number for 4-uniform tight cycles
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866929500430794752 |
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| author | Lo, Allan Pfenninger, Vincent |
| author_facet | Lo, Allan Pfenninger, Vincent |
| contents | A $k$-uniform tight cycle is a $k$-graph with a cyclic ordering of its vertices such that its edges are precisely the sets of $k$ consecutive vertices in that ordering. A $k$-uniform tight path is a $k$-graph obtained by deleting a vertex from a $k$-uniform tight cycle. We prove that the Ramsey number for the $4$-uniform tight cycle on $4n$ vertices is $(5 +o(1))n$. This is asymptotically tight. This result also implies that the Ramsey number for the $4$-uniform tight path on $n$ vertices is $(5/4 + o(1))n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_05276 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The Ramsey number for 4-uniform tight cycles Lo, Allan Pfenninger, Vincent Combinatorics 05C65, 05C35, 05D10 A $k$-uniform tight cycle is a $k$-graph with a cyclic ordering of its vertices such that its edges are precisely the sets of $k$ consecutive vertices in that ordering. A $k$-uniform tight path is a $k$-graph obtained by deleting a vertex from a $k$-uniform tight cycle. We prove that the Ramsey number for the $4$-uniform tight cycle on $4n$ vertices is $(5 +o(1))n$. This is asymptotically tight. This result also implies that the Ramsey number for the $4$-uniform tight path on $n$ vertices is $(5/4 + o(1))n$. |
| title | The Ramsey number for 4-uniform tight cycles |
| topic | Combinatorics 05C65, 05C35, 05D10 |
| url | https://arxiv.org/abs/2111.05276 |