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

Abstract

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.