• Login
    View Item 
    •   Home
    • UA Graduate and Undergraduate Research
    • UA Theses and Dissertations
    • Dissertations
    • View Item
    •   Home
    • UA Graduate and Undergraduate Research
    • UA Theses and Dissertations
    • Dissertations
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Browse

    All of UA Campus RepositoryCommunitiesTitleAuthorsIssue DateSubmit DateSubjectsPublisherJournalThis CollectionTitleAuthorsIssue DateSubmit DateSubjectsPublisherJournal

    My Account

    LoginRegister

    About

    AboutUA Faculty PublicationsUA DissertationsUA Master's ThesesUA Honors ThesesUA PressUA YearbooksUA CatalogsUA Libraries

    Statistics

    Most Popular ItemsStatistics by CountryMost Popular Authors

    Unlabled Level Planarity

    • CSV
    • RefMan
    • EndNote
    • BibTex
    • RefWorks
    Thumbnail
    Name:
    azu_etd_10337_sip1_m.pdf
    Size:
    1.662Mb
    Format:
    PDF
    Description:
    azu_etd_10337_sip1_m.pdf
    Download
    Author
    Fowler, Joe
    Issue Date
    2009
    Keywords
    Graph drawing
    Level planarity
    Simultaneous embedding
    ULP graphs
    Unlabaled level planarity
    Advisor
    Kobourov, Stephen G.
    Committee Chair
    Kobourov, Stephen G.
    
    Metadata
    Show full item record
    Publisher
    The University of Arizona.
    Rights
    Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
    Abstract
    Consider a graph G with vertex set V in which each of the n vertices is assigned a number from the set {1, ..., k} for some positive integer k. This assignment phi is a labeling if all k numbers are used. If phi does not assign adjacent vertices the same label, then phi partitions V into k levels. In a level drawing, the y-coordinate of each vertex matches its label and the edges are drawn strictly y-monotone. This leads to level drawings in the xy-plane where all vertices with label j lie along the line lj = {(x, j) : x in Reals} and where each edge crosses any of the k horizontal lines lj for j in [1..k] at most once. A graph with such a labeling forms a level graph and is level planar if it has a level drawing without crossings.We first consider the class of level trees that are level planar regardless of their labeling. We call such trees unlabeled level planar (ULP). We describe which trees are ULP and provide linear-time level planar drawing algorithms for any labeling. We characterize ULP trees in terms of two forbidden subdivisions so that any other tree must contain a subtree homeomorphic to one of these. We also provide linear-time recognition algorithms for ULP trees. We then extend this characterization to all ULP graphs with five additional forbidden subdivisions, and provide linear-time recogntion and drawing algorithms for any given labeling.
    Type
    text
    Electronic Dissertation
    Degree Name
    Ph.D.
    Degree Level
    doctoral
    Degree Program
    Computer Science
    Graduate College
    Degree Grantor
    University of Arizona
    Collections
    Dissertations

    entitlement

     
    The University of Arizona Libraries | 1510 E. University Blvd. | Tucson, AZ 85721-0055
    Tel 520-621-6442 | repository@u.library.arizona.edu
    DSpace software copyright © 2002-2017  DuraSpace
    Quick Guide | Contact Us | Send Feedback
    Open Repository is a service operated by 
    Atmire NV
     

    Export search results

    The export option will allow you to export the current search results of the entered query to a file. Different formats are available for download. To export the items, click on the button corresponding with the preferred download format.

    By default, clicking on the export buttons will result in a download of the allowed maximum amount of items.

    To select a subset of the search results, click "Selective Export" button and make a selection of the items you want to export. The amount of items that can be exported at once is similarly restricted as the full export.

    After making a selection, click one of the export format buttons. The amount of items that will be exported is indicated in the bubble next to export format.