LE3 .A278 2012

2012

Clarke, Nancy

Acadia University

Bachelor of Science

Honours

Mathematics and Statistics

Mathematics & Statistics

In this thesis an adapted version of the game Cops and Robber will be discussed. This adaptation will be referred to as Ambush Cops and Robbers. We will start the thesis by discussing previous ideas about Cops and Robber, focusing on those presented by Nowakowski and Winkler as well as Quilliot. We will then move into a discussion of the Copwin Strategy as introduced by Clarke. Next we will move into the adapted version of the game, Ambush Cops and Robbers. It is first necessary to define the rules of the new game. We will then consider various results that are obtained as a consequence of the new rules and distinguish between ambush robberwin graphs and ambush copwin graphs, making particular note of those graphs that change from copwin to robberwin, and conversely, under the new rules. Next we will present a strategy, the Ambush Copwin Strategy, that can be used to win on such graphs. In developing such a strategy it is important to consider the troublesome situations that the cop would encounter, as well as a useful class of graphs to play such a strategy on. Also some “good moves” will be developed for use in a troublesome situation. Finally, the thesis will be concluded by a discussion of the role of a second cop in the game Ambush Cops and Robbers.

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https://scholar.acadiau.ca/islandora/object/theses:907