Towards a splitter theorem for internally 4-connected binary matroids VIII: Small matroids

摘要

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 AP is an internally 4-connected matroid such that M has a proper M'-minor and M' has an N-minor, then vertical bar E(M)vertical bar - vertical bar E(M')vertical bar > 3. The analysis in the splitter theorem requires the constraint vertical bar E(M)vertical bar >= 16. In this article, we complement that analysis by describing all such pairs for which vertical bar E(M)vertical bar <= 15. (C) 2016 Elsevier Inc. All rights reserved.