Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

Abstract

This dissertation explores the structural properties of graphs by extending the classical result of Tutte's Wheel Theorem. In particular, we develop an improved version of Tutte's Wheel Theorem along with new chain theorems for subclasses of 3-connected graphs. These chain theorems provide a systematic approach to characterizing graphs that exclude certain minors, leading to significantly shorter proofs of established results.

In Chapter 5, we present a generalization of the block-tree theorem for connected graphs, which removes the restriction on cut vertices and allows greater flexibility in separator sizes. By integrating the results from Chapters 3, 4, and 5, we obtain a more concise proof for two characterizations: one for 3-connected graphs with no Prism minor and another for 3-connected graphs with no W5 minor.

Date

4-2-2025

Committee Chair

Ding, Guoli

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