• About
    • Login
    View Item 
    •   Institutional Repository Home
    • Electronic Theses and Dissertations
    • Electronic Theses and Dissertations
    • View Item
    •   Institutional Repository Home
    • Electronic Theses and Dissertations
    • Electronic Theses and Dissertations
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Browse

    All of Institutional RepositoryCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsDepartmentThis CollectionBy Issue DateAuthorsTitlesSubjectsDepartment

    My Account

    LoginRegister

    On the fine structure of graphs avoiding certain complete bipartite minors

    Solava, Ryan William
    : https://etd.library.vanderbilt.edu/etd-08182019-190904
    http://hdl.handle.net/1803/13941
    : 2019-08-19

    Abstract

    Avoiding complete bipartite graphs as minors, and in particular $K_{2,t}$ as a minor, has been used to give sufficient conditions for Hamiltonicity. For this reason and others, the classes of $K_{2,t}$-minor-free graphs are of interest. Ding gave a rough description of the $K_{2,t}$-minor-free graphs that gives necessary conditions for a graph to be $K_{2,t}$-minor-free. We refine this description and characterize the $K_{2,t}$-minor-free graphs in the 3- and 4-connected cases, giving necessary and sufficient conditions. We also give a program for characterizing the 3-connected $K_{2,5}$-minor-free graphs. As part of this program, we prove a result on fan expansions that is of independent interest.
    Show full item record

    Files in this item

    Icon
    Name:
    solava_dissertation.pdf
    Size:
    458.9Kb
    Format:
    PDF
    View/Open

    This item appears in the following collection(s):

    • Electronic Theses and Dissertations

    Connect with Vanderbilt Libraries

    Your Vanderbilt

    • Alumni
    • Current Students
    • Faculty & Staff
    • International Students
    • Media
    • Parents & Family
    • Prospective Students
    • Researchers
    • Sports Fans
    • Visitors & Neighbors

    Support the Jean and Alexander Heard Libraries

    Support the Library...Give Now

    Gifts to the Libraries support the learning and research needs of the entire Vanderbilt community. Learn more about giving to the Libraries.

    Become a Friend of the Libraries

    Quick Links

    • Hours
    • About
    • Employment
    • Staff Directory
    • Accessibility Services
    • Contact
    • Vanderbilt Home
    • Privacy Policy