Our splitter theorem studies pairs of the form (M,N), where M and N are internally 4-connected binary matroids, M has a proper N-minor, and if M' is an internally 4-connected matroid such that M has a proper M'-minor and M' has an N-minor, then |E(M)|−|E(M')|>3. The analysis in the splitter theorem requires the constraint |E(M)|≥16. In this article, we complement that analysis by describing all such pairs for which |E(M)|≤15.
Publication Source (Journal or Book title)
Advances in Applied Mathematics
Chun, C., Mayhew, D., & Oxley, J. (2017). Towards a splitter theorem for internally 4-connected binary matroids VIII: Small matroids. Advances in Applied Mathematics, 85, 12-30. https://doi.org/10.1016/j.aam.2016.11.009