In this paper, we give a complete characterization of binary matroids with no P9-minor. A 3-connected binary matroid M has no P9-minor if and only if M is a 3-connected regular matroid, a binary spike with rank at least four, one of the internally 4-connected non-regular minors of a special 16-element matroid Y16, or a matroid obtained by 3-summing copies of the Fano matroid to a 3-connected cographic matroid M∗(K3,n), M∗(K3,n'), M∗(K3,n''), or M∗(K3,n''') (n ≥ 2). Here the simple graphs K3,n', K3,n'', and K3,n''' are obtained from K3,n by adding one, two, or three edges in the color class of size three, respectively.
Publication Source (Journal or Book title)
Advances in Applied Mathematics
Ding, G., & Wu, H. (2015). Characterizing binary matroids with no P9-minor. Advances in Applied Mathematics, 70, 70-91. https://doi.org/10.1016/j.aam.2015.07.001