A splitter theorem for internally 4-connected binary matroids: small matroids

Carolyn Chun, Dillon Mayhew, James Oxley

Published 2015-01-01Version 1

Our splitter theorem for internally 4-connected binary matroids studies pairs of the form (N,M), where N and M are internally 4-connected binary matroids, M has a proper N-minor and there is no internally 4-connected matroid that lies strictly between N and M in the minor-order on binary matroids. The analysis in the splitter theorem requires the constraint that |E(M)|>15. In this technical report, we complement that analysis by using an exhaustive search to find all such pairs satisfying 5 < |E(N)| < |E(M)|-3 < |E(M)| < 16.