Dean, Nathaniel2009-06-042009-06-042001Venkataraman, Sripriya. "Survey of results in impartial combinatorial games and an extension to three-player game." (2001) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/17477">https://hdl.handle.net/1911/17477</a>.https://hdl.handle.net/1911/17477There are several known methods to find winning strategies for two-player combinatorial games. This thesis surveys results known for two-player combinatorial games and elucidates a particular winning strategy for a three player game using graph theory. The motivation for work in this area is a belief on the ability of graph theoretic tools to handle multi-player combinatorial game analyses. A winning strategy for two-player undirected vertex Geography game has been formulated earlier and has been shown to be polynomial time. This thesis extends the result to three-player undirected vertex Geography, played on directed trees and answers the question "Does the first player have a winning strategy?". The extension serves as a platform for generalizing results to games involving more than three players.41 p.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.MathematicsStatisticsThesisTHESIS MATH.SCI. 2001 VENKATARAMAN