2 problems

Asymptotic monotonicity conjecture. The Avoider-Enforcer non-planarity, non-$k$-colorability and $K_t$-minor games are asymptotically monotone for every $k\geq 3$ and $t\geq 4$.

Let $H$ be a fixed graph. In the Avoider-Enforcer game on the edge set of $K_n$, let ${\mathcal K}_H$ be the family of all copies of $H$, and let $f^-_{{\mathcal K}_H}$ and…