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We say $G$ is Ramsey size linear if $R(G,H)\ll m$ for all graphs $H$ with $m$ edges and no isolated vertices.

Are there infinitely many graphs $G$ which are not Ramsey size linear but such that all of its subgraphs are?

Asked by Erdős, Faudree, Rousseau, and Schelp [EFRS93]. $K_4$ is the only known example of such a graph.

Wigderson [Wi24] has proved that there are infinitely many such graphs (although his proof is not explicit, and an explicit example of such a graph apart from $K_4$ is still unknown.)