Adamski, GrzegorzGrzegorzAdamskiBednarska-Bzdęga, MałgorzataMałgorzataBednarska-BzdęgaAntoniuk, SylwiaSylwiaAntoniukHamann, FabianFabianHamannClemens, DennisDennisClemensMogge, YannickYannickMogge2025-09-162025-09-162025-08-22The electronic journal of combinatorics 32 (3): P3.35 (2025)https://hdl.handle.net/11420/57403For a positive integer n and a tree Tn on n vertices, we consider an unbiased Waiter-Client game WC(n, Tn) played on the complete graph Kn, in which Waiter’s goal is to force Client to build a copy of Tn. We prove that for every constant c < 1/3, if ∆(Tn) ≤ cn and n is sufficiently large, then Waiter has a winning strategy in WC(n, Tn). On the other hand, we show that there exist a positive constant c′ < 1/2 and a family of trees Tn with ∆(Tn) ≤ c′n such that Client has a winning strategy in the WC(n, Tn) game for every n sufficiently large. We also consider the corresponding problem in the Client-Waiter version of the game.en1077-892620253Australian National Universityhttps://creativecommons.org/licenses/by-nd/4.0/Natural Sciences and Mathematics::510: MathematicsJournal Articlehttps://doi.org/10.15480/882.1587710.37236/1295710.15480/882.15877Journal Article