Ramsey’s theorem, in the version of Erdős and Szekeres, states that every $2$-coloring of the edges of the complete graph on $\{1,2,\dots ,n\}$ contains a monochromatic clique of order $(1/2)logn$. In this article, we consider two well-studied extensions of Ramsey’s theorem. Improving a result of Rödl, we show that there is a constant $c>0$ such that every $2$-coloring of the edges of the complete graph on $\{2,3,\dots ,n\}$ contains a monochromatic clique $S$ for which the sum of $1/logi$ over all vertices $i\in S$ is at least $clogloglogn$. This is tight up to the constant factor $c$ and answers a question of Erdős from 1981. Motivated by a problem in model theory, Väänänen asked whether for every $k$ there is an $n$ such that the following holds: for every permutation $\pi$ of $1,\dots ,k-1$, every $2$-coloring of the edges of the complete graph on $\{1,2,\dots ,n\}$ contains a monochromatic clique $a_1<\cdots <a_k$ with

$$a_{\pi \left(1\right)+1}-a_{\pi \left(1\right)}>a_{\pi \left(2\right)+1}-a_{\pi \left(2\right)}>\cdots >a_{\pi (k-1)+1}-a_{\pi (k-1)}.$$

That is, not only do we want a monochromatic clique, but the differences between consecutive vertices must satisfy a prescribed order. Alon and, independently, Erdős, Hajnal, and Pach answered this question affirmatively. Alon further conjectured that the true growth rate should be exponential in $k$. We make progress towards this conjecture, obtaining an upper bound on $n$ which is exponential in a power of $k$. This improves a result of Shelah, who showed that $n$ is at most double-exponential in $k$.