Date of Award
8-2010
Document Type
Thesis
Degree Name
Master of Science (MS)
College/School
College of Science and Mathematics
Department/Program
Mathematical Sciences
Thesis Sponsor/Dissertation Chair/Project Chair
Jonathan Cutler
Committee Member
Evan Fuller
Committee Member
Aihua Li
Abstract
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
Recommended Citation
Gupta, Ashish, "Trees in Connected Graphs" (2010). Theses, Dissertations and Culminating Projects. 865.
https://digitalcommons.montclair.edu/etd/865