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    Vertex arboricity of triangle-free graphs

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    Warren_S_2016.pdf
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    Author
    Warren, Samantha
    Chair
    Gimbel, John
    Committee
    Faudree, Jill
    Allman, Elizabeth
    Keyword
    Graph coloring
    Random graphs
    Graph theory
    Metadata
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    URI
    http://hdl.handle.net/11122/8223
    Abstract
    The vertex arboricity of a graph is the minimum number of colors needed to color the vertices so that the subgraph induced by each color class is a forest. In other words, the vertex arboricity of a graph is the fewest number of colors required in order to color a graph such that every cycle has at least two colors. Although not standard, we will refer to vertex arboricity simply as arboricity. In this paper, we discuss properties of chromatic number and k-defective chromatic number and how those properties relate to the arboricity of trianglefree graphs. In particular, we find bounds on the minimum order of a graph having arboricity three. Equivalently, we consider the largest possible vertex arboricity of triangle-free graphs of fixed order.
    Description
    Master's Project (M.S.) University of Alaska Fairbanks, 2016
    Date
    2016-05
    Type
    Master's Project
    Collections
    Mathematics and Statistics

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