The Internally 4-Connected Binary Matroids with No $M(K_{3,3})$-Minor
Jan 2010 · American Mathematical Soc.
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The authors give a characterization of the internally $4$-connected binary matroids that have no minor isomorphic to $M(K_{3,3})$. Any such matroid is either cographic, or is isomorphic to a particular single-element extension of the bond matroid of a cubic or quartic Mobius ladder, or is isomorphic to one of eighteen sporadic matroids.
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