Problem 567

Erdős Problem #567: declared status 'open'. Formalized: yes. Let $G$ be either $Q_3$ or $K_{3,3}$ or $H_5$ (the last formed by adding two vertex-disjoint chords to $C_5$). Is it true that, if $H$ has $m$ edges and no isolated vertices, then$$R(G,H)\ll m?$$ Prize: no. Tags: graph theory, ramsey theory.