3 problems

Logarithmic upper-bound conjecture. If $G$ is tightly connected and is not homomorphic to $F$, then there exists a constant $c$ depending only on $F$ such that, for large enough…

Generalized Erdős–Rogers polynomial-growth conjecture. There exists a constant $c=c(F,G)$ such that

Conlon–Fox–Gunby–He–Mubayi–Suk–Verstraëte–Yu conjecture. There exists a constant $c=c(G)$ such that