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Title: Waiter-Client and Client-Waiter games
Author: Tan, Wei En
ISNI:       0000 0004 6425 1650
Awarding Body: University of Birmingham
Current Institution: University of Birmingham
Date of Award: 2017
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In this thesis, we consider two types of positional games; Waiter-Client and Client-Waiter games. Each round in a biased (a:b) game begins with Waiter offering a+b free elements of the board to Client. Client claims a elements among these and the remaining b elements are claimed by Waiter. Waiter wins in a Waiter-Client game if he can force Client to fully claim a winning set, otherwise Client wins. In a Client-Waiter game, Client wins if he can claim a winning set himself, else Waiter wins. We estimate the threshold bias of four different (1:q) Waiter-Client and Client-Waiter games. This is the unique value of Waiter's bias q at which the player with a winning strategy changes. We find its asymptotic value for both versions of the complete-minor and non-planarity games and give bounds for both versions of the non-r-colourability and k-SAT games. Our results show that these games exhibit a heuristic called the probabilistic intuition. We also find sharp probability thresholds for the appearance of a graph in the random graph G(n,p) on which Waiter and Client win the (1:q) Waiter-Client and Client-Waiter Hamiltonicity games respectively.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics