Excluded minors for the matroids of branch-width 3

Abstract

This thesis considers the problem of finding the excluded minors for the matroids of branch-width 3. It is shown that the excluded minors have at most 14 elements. The excluded minors are divided into three classes, those that are 4-connected, those that are internally 4-connected, and those that contain a 4-element 3-separator. In this thesis, we find all excluded minors containing a 4-element 3-separator. The results of this thesis are obtained using theorems on connectivity.