# 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.