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- W4298045370 abstract "Let $R(G)$ be the two-colour Ramsey number of a graph $G$. In this note, we prove that for any non-decreasing function $n leq f(n) leq R(K_n)$, there exists a sequence of connected graphs $(G_n)_{ninmathbb N}$, with $|V(G_n)| = n$ for all $n geq 1$, such that $R(G_n) = Theta(f(n))$. In contrast, we also show that an analogous statement does not hold for hypergraphs of uniformity at least $5$. We also use our techniques to answer a question posed by DeBiasio about the existence of sequences of graphs whose $2$-colour Ramsey number is linear whereas their $3$-colour Ramsey number has superlinear growth." @default.
- W4298045370 created "2022-10-01" @default.
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- W4298045370 date "2022-09-12" @default.
- W4298045370 modified "2023-09-27" @default.
- W4298045370 title "Ramsey numbers with prescribed rate of growth" @default.
- W4298045370 doi "https://doi.org/10.37236/11652" @default.
- W4298045370 hasPublicationYear "2022" @default.
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