Date of Award
Master of Science (MS)
College of Science and Mathematics
Thesis Sponsor/Dissertation Chair/Project Chair
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.
Gupta, Ashish, "Trees in Connected Graphs" (2010). Theses, Dissertations and Culminating Projects. 865.