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• W2950473491 abstract "For a finite set $X$, a family of sets ${mathcal F} subseteq 2^X$ and a positive integer $q$, we consider two types of two player, perfect information games with no chance moves. In each round of the $(1 : q)$ Waiter-Client game $(X, {mathcal F})$, the first player, called Waiter, offers the second player, called Client, $q+1$ elements of the board $X$ which have not been offered previously. Client then chooses one of these elements which he claims and the remaining $q$ elements to go back to Waiter. Waiter wins this game if by the time every element of $X$ has been claimed by some player, Client has claimed all elements of some $A in {mathcal F}$; otherwise Client is the winner. Client-Waiter games are defined analogously, the main difference being that Client wins the game if he manages to claim all elements of some $A in {mathcal F}$ and Waiter wins otherwise. In this paper we study the Waiter-Client and Client-Waiter versions of the non-planarity, $K_t$-minor and non-$k$-colorability games. For each such game, we give a fairly precise estimate of the unique integer $q$ at which the outcome of the game changes from Client's win to Waiter's win. We also discuss the relation between our results, random graphs, and the corresponding Maker-Breaker and Avoider-Enforcer games." @default.
• W2950473491 created "2019-06-27" @default.
• W2950473491 creator A5008556299 @default.
• W2950473491 creator A5072848658 @default.
• W2950473491 creator A5090732083 @default.
• W2950473491 date "2014-12-03" @default.
• W2950473491 modified "2023-09-27" @default.
• W2950473491 title "Waiter-Client and Client-Waiter planarity, colorability and minor games" @default.
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• W2950473491 hasPublicationYear "2014" @default.
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