Hall, Rhiannon2011-06-212022-10-262011-06-212022-10-2620012001https://ir.wgtn.ac.nz/handle/123456789/24940This 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.pdfen-NZGraph theoryMatroidsMathematicsText