Size-Ramsey numbers of tight paths
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913922247819264 |
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| author | Letzter, Shoham Pokrovskiy, Alexey Yepremyan, Liana |
| author_facet | Letzter, Shoham Pokrovskiy, Alexey Yepremyan, Liana |
| contents | The $s$-colour size-Ramsey number of a hypergraph $H$ is the minimum number of edges in a hypergraph $G$ whose every $s$-edge-colouring contains a monochromatic copy of $H$. We show that the $s$-colour size-Ramsey number of the $r$-uniform tight path on $n$ vertices is linear in $n$, for every fixed $r$ and $s$, thereby answering a question of Dudek, La Fleur, Mubayi and Rödl (2017). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01498 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Size-Ramsey numbers of tight paths Letzter, Shoham Pokrovskiy, Alexey Yepremyan, Liana Combinatorics The $s$-colour size-Ramsey number of a hypergraph $H$ is the minimum number of edges in a hypergraph $G$ whose every $s$-edge-colouring contains a monochromatic copy of $H$. We show that the $s$-colour size-Ramsey number of the $r$-uniform tight path on $n$ vertices is linear in $n$, for every fixed $r$ and $s$, thereby answering a question of Dudek, La Fleur, Mubayi and Rödl (2017). |
| title | Size-Ramsey numbers of tight paths |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2507.01498 |