# Research Topic: Waiter-Client games on random boards

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

### Collaborators (external): Olaf Parczyk

Biased *Waiter-Client games* (formerly known as *Picker-Chooser games*, see e.g.Â [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.

Usually Waiter-Client games are played on a complete graph \(K_n\). Other interesting boards to consider are *random graphs*. For example one can consider a random graph \(G \sim G_{n,p}\) with \(n\) vertices, where each edge is contained in the graph with probabality \(p\). Another option is to consider games on *randomly perturbed graphs*, which are the union of a random graph \(G \sim G_{n,p}\) and a deterministic graph \(G_{\alpha}\) with minimum degree \(\alpha\).