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

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

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    5 Citations (Scopus)
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    © 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
    Issue number3
    Publication statusPublished - Sep 2014


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