Author ORCID Identifier

http://orcid.org/0000-0002-3821-1183

Degree Year

2021

Document Type

Thesis

Degree Name

Bachelor of Arts

Department

Mathematics

Advisor(s)

Elizabeth L. Wilmer

Keywords

Hypercubes, Graphs, Cycles, Models, Color

Abstract

In this paper, we look at two families of graphs, cycles and hypercubes, and compare how their sets of proper 3-colorings differ as the graphs get arbitrarily large. In particular, we find the probability of pairs of vertices at various distances being the same color in order to understand the range and scale of interactions between them. As we look at larger and larger cycles, larger and larger hypercubes, patterns begin to emerge. While the colors of vertices fixed fractions of the cycle away from each other are independent, a random 3-coloring of the hypercube is essentially a 2-coloring. This models how local constraints can propagate very differently through different kinds of networks.

Included in

Mathematics Commons

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