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    Exploring The Thirteen Colorful Variations Of Guthrie's Four-Color Conjecture

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    Title
    Exploring The Thirteen Colorful Variations Of Guthrie's Four-Color Conjecture
    Author
    Keough, Kathryn
    Date
    May 2020
    Subject
    coloring
    four color theorem
    graphs
    math
    regions
    
    Metadata
    Show full item record
    URI
    http://hdl.handle.net/20.500.13013/766
    Abstract
    Coloring is an important part of graph theory. Historically, it was thought that only four colors could be the minimal number of colors. This paper discusses the Four Color Theorem and how the Four Color Theorem is applied to graphs. This paper gives an overview of several different definitions involved with graphs and shows how to create a dual graph. This paper also discusses how a graph of 12 regions has at least one region bounded by less than five edges. The paper includes several figures which include graphs, dual graphs, and different colorings. The paper also provides a proof which shows mathematically why a graph of 12 regions has at least one region bounded by less than five edges.
    Advisor
    Travers, Brian
    Department
    Mathematics
    Degree
    Bachelor of Fine Arts (BFA)
    Collections
    Mathematics Honors Theses
    Honors Theses

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