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The Shannon switching game is a combinatorial game for two players, which we refer to as the cop and the robber. In this project, we explore a few variations of the original rules that make the game more interesting. One of these variations is a game involving multiple cops and one robber. We present a formal recursive definition of this game which we use to prove several basic theoretical results. Next, we consider this game on complete graphs and complete bipartite graphs. On each family of graphs, we investigate the winning conditions for the players depending on who goes first. We describe these conditions as functions and prove several asymptotic results. Finally, after looking at the variation with multiple cops and one robber, we also study the game with multiple cops and multiple robbers and compare the two variations.
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Wood, Kimberly Y., "Switching the Shannon Switching Game" (2012). Senior Projects Spring 2012. 292.