Date of Award
Master of Science (MS)
Mathematics and Statistics
It is a well known fact in graph theory that in a connected graph any two longest paths must have a vertex in common. In this paper we will explore what happens when we look at k - connected graphs, leading us to make a conjecture about the intersection of any two longest paths. We then look at cycles and look at what would be needed to improve on a result by Chen, Faudree and Gould about the intersection of two longest cycles.
Hippchen, Thomas, "Intersections of Longest Paths and Cycles." Thesis, Georgia State University, 2008.