Date of Submission

Spring 2013

Academic Program

Mathematics

Project Advisor 1

Jim Belk

Abstract/Artist's Statement

We study a pursuit game involving one or more pursuers and an invisible target on finite, connected topological graphs. The winning condition for this game leads to a sequence of minor closed properties, and one of our main goals is to characterize the forbidden minors for these properties. We also study simple graphs, multigraphs and topological graphs in the context of this game, and explore the complicated relationship between the forbidden graph characterizations for each. We conclude with some results on how the minor closed properties we are studying are related to pathwidth, one of the main concepts underlying the proof of the Forbidden Minor Theorem. As part of our research, we created a computer program on Processing, an open source programming language, which enables us to interactively play the game on a computer. The code for this program is given in the concluding chapter of this project.

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