Hamiltonian Cycles in Graphs on a Torus
Presentation Type
Poster
Keywords
Combinatorics, Graph Theory
Department
Mathematics
Major
Mathematics
Abstract
Let G be a graph embedded on a surface S. Each cycle in G is an element of a homotopy class of simple closed curves on S. We consider the distribution of Hamiltonian cycles among homotopy classes of curves in the case where S is a torus and G is the edge graph of a regular triangulation of S. We discuss possible explanations for the changing number of Hamiltonian cycles as the number of vertices in the triangulation increases.
Faculty Mentor
Dr. Joshua Bowman
Funding Source or Research Program
Academic Year Undergraduate Research Initiative
Location
Waves Cafeteria
Start Date
25-3-2022 2:00 PM
End Date
25-3-2022 3:00 PM
Hamiltonian Cycles in Graphs on a Torus
Waves Cafeteria
Let G be a graph embedded on a surface S. Each cycle in G is an element of a homotopy class of simple closed curves on S. We consider the distribution of Hamiltonian cycles among homotopy classes of curves in the case where S is a torus and G is the edge graph of a regular triangulation of S. We discuss possible explanations for the changing number of Hamiltonian cycles as the number of vertices in the triangulation increases.