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portada A Hyper Graph Regularity Method for Linear Hypergraphs
Type
Physical Book
Publisher
Author
Year
2011
Language
English
Pages
56
Format
Paperback
ISBN
3844388397
ISBN13
9783844388398
Categories

A Hyper Graph Regularity Method for Linear Hypergraphs

Shoaib Khan; Brendan Nagle (Author) · Lap Lambert Academic Publishing · Paperback

A Hyper Graph Regularity Method for Linear Hypergraphs - Shoaib Khan; Brendan Nagle

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Synopsis "A Hyper Graph Regularity Method for Linear Hypergraphs "

Szemerédi's Regularity Lemma is a 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, Rődl, 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 Szemerédi'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.

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