4 problems

Let $D(n)$ be the largest integer $t$ such that for every tree $T$ with $v(T)=n$ and $\Delta(T)\leq t$, Waiter has a winning strategy in $\operatorname{WC}(n,T)$. Linear asymptotics…

Let $K_n$ be the complete graph on $n$ vertices. A graph is tree-universal at degree bound $D$ if it contains a copy of every tree $T$ with $n$ vertices and maximum degree…

Let $K_n$ be the complete graph on $n$ vertices. In a $(q:1)$ Waiter–Client game on $E(K_n)$, Waiter offers $q+1$ unclaimed edges in each round, and Client claims one offered edge…

Let $K_n$ be the complete graph on $n$ vertices, and let $\mathcal L(n,q)$ denote the largest component size that Waiter can force in Client's graph when playing a $(q:1)$ Waiter–C…