2 problems

Liu–Montgomery's crux conjecture. There exists some constant $c>0$ such that every graph $G$ contains a subdivision of a clique with at least

Clique-subdivision bound. The constant $\frac{2}{3}\log_2 3$ in the equivalent bound $2^{(2/3)\log_2(3)t+o(t)}n$ is conjectured to be best possible.