Maximum size binary matroids with no AG(3, 2)-minor are graphic

J. Kung, D. Mayhew, Irene Pivotto, Gordon Royle

    Research output: Contribution to journalArticle

    4 Citations (Scopus)
    266 Downloads (Pure)

    Abstract

    © 2014 Society for Industrial and Applied Mathematics. We prove that the maximum size of a simple binary matroid of rank r ≥ 5 with no AG(3, 2)-minor is (2 r+1) and characterize those matroids achieving this bound. When r ≥ 6, the graphic matroid M (Kr+1) is the unique matroid meeting the bound, but there are a handful of matroids of lower ranks meeting or exceeding this bound. In addition, we determine the size function for nongraphic simple binary matroids with no AG(3, 2)-minor and characterize the matroids of maximum size for each rank.
    Original languageEnglish
    Pages (from-to)1559-1577
    JournalSIAM Journal on Discrete Mathematics
    Volume28
    Issue number3
    DOIs
    Publication statusPublished - Sep 2014

    Fingerprint Dive into the research topics of 'Maximum size binary matroids with no AG(3, 2)-minor are graphic'. Together they form a unique fingerprint.

    Cite this