Date of Award
Master of Science (MS)
College of Science and Mathematics
Thesis Sponsor/Dissertation Chair/Project Chair
Given a graph G, we study the problem of finding a spanning tree T that maximizes the number of vertices of full degree; that is, the number of vertices whose degree in T equals its degree in G. We prove a few general bounds and then analyze this parameter on various classes of graphs including grid graphs, hypercubes, and random regular graphs. We also explore a related problem that focuses on maximizing the number of leaves in a spanning tree of a graph.
Acquaviva, Sarah, "The Full Degree Spanning Tree Problem" (2023). Theses, Dissertations and Culminating Projects. 1292.