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- W2972248832 abstract "For fixed $s ge 3$, we prove that if optimal $K_s$-free pseudorandom graphs exist, then the Ramsey number $r(s,t)$ is $t^{s-1+o(1)}$ as $t rightarrow infty$. Our method also improves the best lower bounds for $r(C_{ell},t)$ obtained by Bohman and Keevash from the random $C_{ell}$-free process by polylogarithmic factors for all odd $ell geq 5$ and $ell in {6,10}$. For $ell = 4$ it matches their lower bound from the $C_4$-free process. We also prove, via a different approach, that $r(C_5, t)> (1+nobreak o(1))t^{11/8}$ and $r(C_7, t)> (1+nobreak o(1))t^{11/9}$. These improve the exponent of $t$ in the previous best results and appear to be the first examples of graphs $F$ with cycles for which such an improvement of the exponent for $r(F, t)$ is shown over the bounds given by the random $F$-free process and random graphs." @default.
- W2972248832 created "2019-09-12" @default.
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- W2972248832 date "2023-06-12" @default.
- W2972248832 modified "2023-09-25" @default.
- W2972248832 title "A note on pseudorandom Ramsey graphs" @default.
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- W2972248832 doi "https://doi.org/10.4171/jems/1359" @default.
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