4 problems

Projective-plane incidence-graph conjecture. The function $\text{mi}_k(n,\mathcal{F})$ is not bounded above by any polynomial in $n$.

Complete-bipartite-union conjecture. The maximum number of $k$-dominating independent sets in an $n$-vertex graph is attained by the disjoint union of $n/(2k)$ copies of $K_{k,k}$.

Attainment conjecture. For every $k$, there exists a graph $G$ such that

The $\sqrt[9]{6}$-conjecture. The maximal number of $2$-dominating independent sets in $n$-vertex graphs is $\Theta(\sqrt[9]{6}^{\,n})$; equivalently,