2 problems

Let $T$ be a tree of order $n$. Write $a(T)$ for the smallest integer $m$ such that Alice has a winning strategy in the achievement game for $T$ on $K_m$, and let $P_n$ and…

In the planar achievement game, a finite point set $G\subset\mathbb{R}^2$ is used as the goal set: players alternately place points, and Player 1 seeks to build a congruent copy of…