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

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Mar 25th, 2:00 PM Mar 25th, 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.