4 problems

Asymmetric fractalizer conjecture. There exists an asymmetric fractalizer on at most $9$ vertices.

Let $F$ be a complete partite graph. The inducibility problem for $F$ asks for the maximum possible induced $F$-density in graphs of increasing order, and is perfectly stable when…

The Edge-statistics Conjecture. For all integers $k$ and $\ell$ with $0<\ell<{k\choose 2}$,

Let $C_k$ denote the cycle on $k$ vertices. For a graph $H$, its induced density is the number of induced copies of $H$ divided by $\binom{|G|}{|H|}$; write $I(H;n)$ for the maximu…