Survey of results in impartial combinatorial games and an extension to three-player game

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dc.contributor.advisorDean, Nathanielen_US
dc.creatorVenkataraman, Sripriyaen_US
dc.date.accessioned2009-06-04T07:56:38Zen_US
dc.date.available2009-06-04T07:56:38Zen_US
dc.date.issued2001en_US
dc.description.abstractThere 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.en_US
dc.format.extent41 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS MATH.SCI. 2001 VENKATARAMANen_US
dc.identifier.citationVenkataraman, 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>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/17477en_US
dc.language.isoengen_US
dc.rightsCopyright 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.en_US
dc.subjectMathematicsen_US
dc.subjectStatisticsen_US
dc.titleSurvey of results in impartial combinatorial games and an extension to three-player gameen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMathematical Sciencesen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelMastersen_US
thesis.degree.nameMaster of Artsen_US
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