Creating Spanning Trees in Waiter-Client Games

• Published in: The Electronic journal of combinatorics Vol. 32; no. 3
• Main Authors: Adamski, Grzegorz, Antoniuk, Sylwia, Bednarska-Bzdęga, Małgorzata, Clemens, Dennis, Hamann, Fabian, Mogge, Yannick
• Format: Journal Article
• Language: English
• Published: 22.08.2025

For a positive integer $n$ and a tree $T_n$ on $n$ vertices, we consider an unbiased Waiter-Client game $\textrm{WC}(n,T_n)$ played on the complete graph $K_n$, in which Waiter's goal is to force Client to build a copy of $T_n$. We prove that for every constant $c<1/3$, if $\Delta(T_n)\le cn...