Faculty Advisor

Martin, William J.

Faculty Advisor

Sarkozy, Gabor N


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.


Worcester Polytechnic Institute

Date Accepted

April 2015


Mathematical Sciences

Project Type

Major Qualifying Project



Advisor Department

Mathematical Sciences

Advisor Department

Computer Science