The multicolour size Ramsey number of a path
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918450249596928 |
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| author | Beke, Csongor Li, Anqi Sahasrabudhe, Julian |
| author_facet | Beke, Csongor Li, Anqi Sahasrabudhe, Julian |
| contents | In this paper, we determine the $r$-colour size Ramsey number of the path $P_k$, up to constants. In particular, for every fixed $r \geq 2$ and $k \geq 100\log r$, we have
\[ \widehat{R}_r(P_k)=Θ((r^2 \log r) \, k).\] Perhaps surprisingly, we do this by improving the lower bound on $\widehat{R}_r(P_k)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_16656 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The multicolour size Ramsey number of a path Beke, Csongor Li, Anqi Sahasrabudhe, Julian Combinatorics In this paper, we determine the $r$-colour size Ramsey number of the path $P_k$, up to constants. In particular, for every fixed $r \geq 2$ and $k \geq 100\log r$, we have \[ \widehat{R}_r(P_k)=Θ((r^2 \log r) \, k).\] Perhaps surprisingly, we do this by improving the lower bound on $\widehat{R}_r(P_k)$. |
| title | The multicolour size Ramsey number of a path |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2511.16656 |