Date of Award

6-2020

Document Type

Thesis

Degree Name

Master of Arts in Mathematics

Department

Mathematics

First Reader/Committee Chair

Dr. Aikin, Jeremy

Abstract

Matroids are discrete mathematical objects that generalize important concepts of independence arising in other areas of mathematics. There are many different important classes of matroids and a frequent problem in matroid theory is to determine whether or not a given matroid belongs to a certain class of matroids. For special classes of matroids that are minor-closed, this question is commonly answered by determining a complete list of matroids that are not in the class but have the property that each of their proper minors is in the class; that is, minor-minimal matroids that are not in the minor-closed class. These minor-minimal matroids that are not in the minor-closed class are called excluded minors. In this thesis, we construct interesting minor-closed classes of matroids and then characterize them by determining their complete sets of excluded minors.

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