4 problems

Erdős–Faudree–Sós conjecture. Every $n$-vertex graph $G$ with $\text{hom}(G)=O(\log n)$ satisfies

Narayanan–Tomon conjecture. If $\text{hom}(G)\geq n^{1/2}$, then

Conjectured distinct-degrees bound. One should have

Bukh–Sudakov's conjecture. If