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    Implementing path coloring algorithms on planar graphs

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    Author
    Bross, Daniel Aven
    Chair
    Chappell, Glenn
    Committee
    Lawlor, Orion
    Hartman, Chris
    Keyword
    Graph algorithms
    Algorithms
    Computer algorithms
    Graph coloring
    Metadata
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    URI
    http://hdl.handle.net/11122/8002
    Abstract
    A path coloring of a graph partitions its vertex set into color classes such that each class induces a disjoint union of paths. In this project we implement several algorithms to compute path colorings of graphs embedded in the plane. We present two algorithms to path color plane graphs with 3 colors based on a proof by Poh in 1990. First we describe a naive algorithm that directly follows Poh's procedure, then we give a modified algorithm that runs in linear time. Independent results of Hartman and Skrekovski describe a procedure that takes a plane graph G and a list of 3 colors for each vertex, and computes a path coloring of G such that each vertex receives a color from its list. We present a linear time implementation based on Hartman and Skrekovski's proofs. A C++ implementation is provided for all three algorithms, utilizing the Boost Graph Library. Instructions are given on how to use the implementation to construct colorings for plane graphs represented by Boost data structures.
    Description
    Master's Project (M.S.) University of Alaska Fairbanks, 2017
    Date
    2017-08
    Type
    Master's Project
    Collections
    Computer Science

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