Graduation Year


Document Type




Degree Granting Department

Mathematics and Statistics

Major Professor

Brendan Nagle, Ph.D.


Regularity lemma, Counting lemma, Forbidden families, F-counting algorithm, Constructive removal lemma


Szemerédi's Regularity Lemma is powerful tool in Graph Theory, yielding many applications in areas such as Extremal Graph Theory, Combinatorial Number Theory and Theoretical Computer Science. Strong hypergraph extensions of graph regularity techniques were recently given by Nagle, Rödl, Schacht and Skokan, by W.T. Gowers, and subsequently, by T. Tao. These extensions have yielded quite a few non-trivial applications to Extremal Hypergraph Theory, Combinatorial Number Theory and Theoretical Computer Science. A main drawback to the hypergraph regularity techniques above is that they are highly technical. In this thesis, we consider a less technical version of hypergraph regularity which more directly generalizes Szemeredi's regularity lemma for graphs. The tools we discuss won't yield all applications of their stronger relatives, but yield still several applications in extremal hypergraph theory (for so-called linear or simple hypergraphs), including algorithmic ones. This thesis surveys these lighter regularity techiques, and develops three applications of them.