Date of Award
Master of Arts in Mathematics
First Reader/Committee Chair
Dr. Aikin, Jeremy
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.
Lara Tejeda, Jonathan, "Exploring Matroid Minors" (2020). Electronic Theses, Projects, and Dissertations. 1098.