Over the past decade Laszlo Lovasz has led the development of a new language for talking about large graphs and networks. It opens up new doors for analyzing large graphs and has many connections with classical graph theory results such as the Szemeredi Regularity Lemma. In this project I sought to understand and expand on some of the major concepts expressed in the new language. I prove several theorems concerning homomorphism densities and also look into graphons, the limit objects of Cauchy sequences of graphs. I study them in general and then look at the specific ones that are derived from variations of the Sierpinski carpet fractal.

• This report represents the work of one or more WPI undergraduate students submitted to the faculty as evidence of completion of a degree requirement. WPI routinely publishes these reports on its website without editorial or peer review.

Creator

• Steele, Corre Love

Publisher

• Worcester Polytechnic Institute

Identifier

• E-project-043015-170021

Advisor

• Sarkozy, Gabor N
• Martin, William J.

Year

• 2015

Date created

• 2015-04-30

Resource type

• Major Qualifying Project

Major

• Mathematical Sciences

Rights statement

• In Copyright