A Hyper graph Regularity Method for Linear Hypergraphs: With Applications - Couverture souple

Khan, Shoaib; Nagle, Brendan

 
9783844388398: A Hyper graph Regularity Method for Linear Hypergraphs: With Applications
Couverture souple
ISBN 10 : 3844388397 ISBN 13 : 9783844388398
Editeur : LAP LAMBERT Academic Publishing, 2011

Synopsis

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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Présentation de l'éditeur

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.

Biographie de l'auteur

MA Mathematics, University of South Florida, Tampa FL. Fulbright Scholar. Fields of research: discrete structures, combinatorics, graphs/hypergraphs, logic and computation. Currently serving as Lecturer of Computer Science at National University of Computer & Emerging Sciences, Lahore, Pakistan. (email: shoaib.amjad@nu.edu.pk)

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
LAP LAMBERT Academic Publishing
Date d'édition
2011
Langue
anglais
ISBN 10 
3844388397
ISBN 13 
9783844388398
Reliure
Broché
Nombre de pages
56
Coordonnées du fabricant
non disponible
Personne responsable
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