#### Presentation Title

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.