Date of Award

8-2026

Document Type

Thesis

Degree Name

Master of Arts in Mathematics

Department

Mathematics

First Reader/Committee Chair

Aikin, Jeremy

Abstract

A matroid is a discrete mathematical object that abstracts and connects the various notions of independence found throughout mathematics. Such notions of independence include linear independence, algebraic independence, as well as notions of independence that arise in graph theory. There are many broad classes of matroids. Important examples include binary matroids, graphic matroids, regular matroids, uniform matroids, and various levels of connected matroids. Some of the most important problems in matroid theory involve characterizing classes of matroids so that such characterizations can be used to prove results concerning these matroid classes. This thesis is a study of two important classes of matroids: round matroids and 3-connected matroids. Matroids that are 3-connected cannot be easily decomposed into smaller components, while round matroids are one way to generalize complete graphs in graph theory. In this thesis, we study the relationship between 3-connectedness and roundness in matroid theory.

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