5 problems

Let $D_{CW}(n)$ be the largest integer $t$ such that for every tree $T$ with $v(T)=n$ and $Delta(T)\leq t$, Client can build a red copy of $T$ in $K_n$. Linear-over-logarithmic low…

Let $K_n$ be the complete graph on $n$ vertices. In the $(1:1)$ Client–Waiter game, Waiter offers two board elements at each round and Client claims one; Client's claimed edges for…

Let $\mathcal{OC}_n$ denote the family of odd cycles on the board of the Client-Waiter game, and let $b_{cw}(\mathcal{OC}_n)$ be its threshold bias. Hefetz, Krivelevich and Tan's c…

Let $H$ be a graph, and let $m(H)$ denote the graph parameter used in the critical-bias formulation. The critical bias is the threshold bias $q$ for the Client-Waiter game…

Let $K_n$ be the complete graph on $n$ vertices, let $P_k$ be the path on $k$ vertices, and write $CW(K_n,P_k,Cn)$ for the Client-Waiter game with bias $Cn$ in which Client aims to…