  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 $(G_n)_{n\in\mathbb N}$, 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.
