Ramsey numbers of cycles in random graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866916363302338560 |
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| author | Araújo, Pedro Pavez-Signé, Matías Sanhueza-Matamala, Nicolás |
| author_facet | Araújo, Pedro Pavez-Signé, Matías Sanhueza-Matamala, Nicolás |
| contents | Let $R(C_n)$ be the Ramsey number of the cycle on $n$ vertices. We prove that, for some $C > 0$, with high probability every $2$-colouring of the edges of $G(N,p)$ has a monochromatic copy of $C_n$, as long as $N\geq R(C_n) + C/p$ and $p \geq C/n$. This is sharp up to the value of $C$ and it improves results of Letzter and of Krivelevich, Kronenberg and Mond. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_13028 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Ramsey numbers of cycles in random graphs Araújo, Pedro Pavez-Signé, Matías Sanhueza-Matamala, Nicolás Combinatorics Let $R(C_n)$ be the Ramsey number of the cycle on $n$ vertices. We prove that, for some $C > 0$, with high probability every $2$-colouring of the edges of $G(N,p)$ has a monochromatic copy of $C_n$, as long as $N\geq R(C_n) + C/p$ and $p \geq C/n$. This is sharp up to the value of $C$ and it improves results of Letzter and of Krivelevich, Kronenberg and Mond. |
| title | Ramsey numbers of cycles in random graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2208.13028 |