# Fast Strategies in Waiter-Client games

### Collaborators (MAT): Dr. Dennis Clemens, Fabian Hamann, M. Sc., Yannick Mogge, M. Sc.

### Collaborators (external): Pranshu Gupta, Alexander Haupt, Mirjana Mikalački

Biased *Waiter-Client games* (formerly known as *Picker-Chooser games*, see e.g. [a]) are a variant of Maker-Breaker games, in which during each round Waiter offers to Client \(b+1\) unclaimed elements of which Client claims one element, while the rest go to Waiter. If by the end of the game Waiter could *force* Client to occupy all elements of some winning set, she wins the game, otherwise Client wins.

One option now is to consider *fast strategies*. Here the question is not only if Waiter can win a specific game, but also how fast she can win. If the size of a the smallest winning set coincides with the number of turns, in which Waiter is able to win, we say that the game is won *perfectly fast*, if she only requires a constant number of additional turns, we say the game is won *asymptotically fast*.

## References

[CGHHMM2020] D. Clemens, P. Gupta, F. Hamann, A. Haupt, M. Mikalački, and Y. Mogge. *Fast Strategies in Waiter-Client Games*, The Electronic Journal of Combinatorics 27 (2020), no. 3, P3.57.

[V2021] V. Dvořák, *Waiter-Client Triangle-Factor Game on the Edges of the Complete Graph*, European Journal of Combinatorics 96 (2021), 103356.