Date of Defense
4-19-2017
Date of Graduation
4-2017
Department
Mathematics
First Advisor
Andrzej Dudek
Second Advisor
Patrick Bennett
Third Advisor
Allen Schwenk
Abstract
The regularity lemma (also known as Szemerédi's Regularity Lemma) is one of the most powerful tools used in extremal graph theory. In general, the lemma states that every graph has some structure. That is, every graph can be partitioned into a finite number of classes in a way such that the number of edges between any two parts is “regular." This thesis is an introduction to the regularity lemma through its proof and applications. We demonstrate its applications to extremal graph theory, Ramsey theory, and number theory.
Recommended Citation
Sprangel, Elizabeth, "The Regularity Lemma and its Applications" (2017). Honors Theses. 2802.
https://scholarworks.wmich.edu/honors_theses/2802
Access Setting
Honors Thesis-Open Access