Date of Award


Degree Type


Degree Name

Master of Science (MS)


Mathematics and Statistics

First Advisor

Guantao Chen

Second Advisor

Johannes Hattingh

Third Advisor

Frank Hall

Fourth Advisor

Yi Zhao


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.

Included in

Mathematics Commons