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Excluded minors for the matroids of branch-width 3

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Date

2001

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Te Herenga Waka—Victoria University of Wellington

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.

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Keywords

Graph theory, Matroids, Mathematics

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