Date of Award


Document Type


Degree Name

Master of Science (MS)


College of Science and Mathematics


Mathematical Sciences

Thesis Sponsor/Dissertation Chair/Project Chair

Jonathan Cutler

Committee Member

Evan Fuller

Committee Member

Aihua Li


The focus of the Master’s Thesis will be the investigation of current research involving trees that cover subsets of the vertex set of a connected graph. The primary goal is the extension of some recent results and a conjecture of Horak and McAvaney. Given certain conditions, we will reformulate their conjecture that states that if a graph can be spanned by a number of edge-disjoint trees, we can provide a bound on the maximum degree of this collection of edge-disjoint trees. We are able to show that this conjecture is true if the number of trees used to span the graph is one. We will then look at a specific class of graphs, namely series-parallel graphs, and present several new extremal examples to show that these ”tree-like” graphs are difficult to analyze. A comprehensive survey of related literature is also included.

File Format


Included in

Mathematics Commons