Let be the Ramsey number of the cycle on vertices. We prove that, for some , with high probability every 2‐coloring of the edges of has a monochromatic copy of , as long as and . This is sharp up to the value of and it improves results of Letzter and of Krivelevich, Kronenberg, and Mond.
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Araújo et al. (2024) studied this question.
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