An Exploration of Algebraic Approaches to Graph Theory

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dc.contributorRobinson, Margaret
dc.contributorSt. John, Audrey
dc.contributor.advisorSidman, Jessica
dc.contributor.authorUrbschat, Maya
dc.date.accessioned2016-05-31T16:44:35Z
dc.date.available2016-05-31T16:44:35Z
dc.date.gradyear2016en_US
dc.date.issued2016-05-31
dc.description.abstractIn a 2010 paper, De Loera et al. explore the use of polynomial ideals to determine properties of graphs. Here we present an exposition of the results in said paper on k-colorability and Hamiltonicity of graphs, as well as the improvements on these results made by Li et al. in 2015. We provide detail and background necessary for an undergraduate reader. Additionally, we provide an explicit formula for the Nullstellensatz certificate of non-2-colorability of a graph, and find the graph with smallest order that has a linear Nullstellensatz certificate of non-3-colorability but does not contain an odd wheel.en_US
dc.description.sponsorshipMathematics & Statisticsen_US
dc.identifier.urihttp://hdl.handle.net/10166/3755
dc.language.isoen_USen_US
dc.rights.restrictedpublicen_US
dc.subjectgraph theoryen_US
dc.subjectcommutative algebraen_US
dc.subjectnullstellensatzen_US
dc.subjectgraph coloringen_US
dc.subjecthamiltonian graphsen_US
dc.titleAn Exploration of Algebraic Approaches to Graph Theoryen_US
dc.typeThesis
mhc.degreeUndergraduateen_US
mhc.institutionMount Holyoke College

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