Characterizing binary matroids with no P 9 - minor
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چکیده
3 In this paper, we give a complete characterization of binary matroids 4 with no P9-minor. A 3-connected binary matroid M has no P9-minor 5 if and only if M is one of the internally 4-connected non-regular minors 6 of a special 16-element matroid Y16, a 3-connected regular matroid, a 7 binary spike with rank at least four, or a matroid obtained by 3-summing 8 copies of the Fano matroid to a 3-connected cographic matroid M(K3,n), 9 M∗(K ′ 3,n), M ∗(K ′′ 3,n), or M ∗(K ′′′ 3,n) (n ≥ 2). Here the simple graphs 10 K ′ 3,n,K ′′ 3,n, and K ′′′ 3,n are obtained from K3,n by adding one, two, or 11 three edges in the color class of size three, respectively. 12
منابع مشابه
5 F eb 2 00 9 The Internally 4 - Connected Binary Matroids With No M ( K 3 , 3 ) - Minor . Dillon Mayhew Gordon Royle
We give a characterization of the internally 4-connected binary matroids that have no minor isomorphic to M(K3,3). Any such matroid is either cographic, or is isomorphic to a particular single-element extension of the bond matroid of a cubic or quartic Möbius ladder, or is isomorphic to one of eighteen sporadic matroids. 2000 Mathematics Subject Classification. 05B35.
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تاریخ انتشار 2014