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A Hyper graph Regularity Method for Linear Hypergraphs: With Applications - Shoaib Khan,Brendan Nagle

Anglų
2011-09-19
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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, R¿dl, Schacht and Skokan, by W.T. Gowers, and subsequently, by T. Tao. These extensions have yielded quite a few non-trivial a ... Visas aprašymas

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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, R¿dl, 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.

Daugiau informacijos

Autorius Shoaib Khan, Brendan Nagle
Leidėjas LAP LAMBERT Academic Publishing
Išleidimo metai 2011
Viršelio tipas Minkšti viršeliai
EAN 9783844388398
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52,90 € 70,53 €