• Login
    View Item 
    •   SMARTech Home
    • College of Sciences (CoS)
    • School of Mathematics
    • School of Mathematics Colloquia
    • View Item
    •   SMARTech Home
    • College of Sciences (CoS)
    • School of Mathematics
    • School of Mathematics Colloquia
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Large girth approximate Steiner triple systems

    Thumbnail
    View/Open
    warnke.mp4 (443.1Mb)
    warnke_videostream.html (1.013Kb)
    transcription.txt (40.28Kb)
    thumbnail.jpg (159.9Kb)
    Date
    2018-09-28
    Author
    Warnke, Lutz
    Metadata
    Show full item record
    Abstract
    In 1973 Erdos asked whether there are n-vertex partial Steiner triple systems with arbitrary high girth and quadratically many triples. (Here girth is defined as the smallest integer g \ge 4 for which some g-element vertex-set contains at least g-2 triples.) We answer this question, by showing existence of approximate Steiner triple systems with arbitrary high girth. More concretely, for any fixed \ell \ge 4 we show that a natural constrained random process typically produces a partial Steiner triple system with (1/6-o(1))n^2 triples and girth larger than \ell. The process iteratively adds random triples subject to the constraint that the girth remains larger than \ell. Our result is best possible up to the o(1)-term, which is a negative power of n. Joint work with Tom Bohman.
    URI
    http://hdl.handle.net/1853/60470
    Collections
    • School of Mathematics Colloquia [6]

    Browse

    All of SMARTechCommunities & CollectionsDatesAuthorsTitlesSubjectsTypesThis CollectionDatesAuthorsTitlesSubjectsTypes

    My SMARTech

    Login

    Statistics

    View Usage StatisticsView Google Analytics Statistics
    facebook instagram twitter youtube
    • My Account
    • Contact us
    • Directory
    • Campus Map
    • Support/Give
    • Library Accessibility
      • About SMARTech
      • SMARTech Terms of Use
    Georgia Tech Library266 4th Street NW, Atlanta, GA 30332
    404.894.4500
    • Emergency Information
    • Legal and Privacy Information
    • Human Trafficking Notice
    • Accessibility
    • Accountability
    • Accreditation
    • Employment
    © 2020 Georgia Institute of Technology