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arXiv · 2208.13028

Ramsey numbers of cycles in random graphs

Pedro Araújo·Matías Pavez-Signé·Nicolás Sanhueza-Matamala
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Abstract

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.

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Pedro Araújo, Matías Pavez-Signé, Nicolás Sanhueza-Matamala. 2024-08-20. Ramsey numbers of cycles in random graphs. https://arxiv.org/abs/2208.13028

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