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Extremal Graph Theory for Minors, Improper Colourings and Gonality

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thesis
posted on 12.03.2019 by KEVIN JOHN HENDREY
A graph, consists of a collection of vertices, some of which are joined by edges. Graphs are extremely useful for modelling and solving a wide range of real world problems, from traffic congestion to scheduling problems. We answer several questions about abstract graphs. We show that if a graph has five times as many edges as vertices, then it contains a structure known as a Petersen Minor, and present a formula for generating bounds of this form. We also find new results for variants of vertex colourings, and answer three recently posed questions about a chip firing game on graphs.

History

Campus location

Australia

Principal supervisor

David Wood

Additional supervisor 1

Daniel Horsley

Year of Award

2019

Department, School or Centre

Mathematical Sciences

Course

Doctor of Philosophy

Degree Type

DOCTORATE

Faculty

Faculty of Science

Exports

Exports