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Szemerédi’s Regularity Lemma and Quasi-randomness

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Recent Advances in Algorithms and Combinatorics

Abstract

A beautiful result of Szemerédi on the asymptotic structure of graphs is his regularity lemma. Roughly speaking, this result tells us that any large graph may be written as a union of induced, random looking bipartite graphs. There are many applications of this result—the reader is urged to consult the excellent survey of Komlos and Simonovits [48] for a thorough discussion on this fundamental result.

Partially supported by MCT/CNPq through ProNEx Programme (Proc. CNPq 664107/1997-4), by CNPq (Proc. 300334/93-1 and 468516/2000-0), and by FAPESP (Proj. 96/04505-2)

Partially supported by NSF Grant 0071261

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Authors
  1. Y. Kohayakawa
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  2. V. Rödl
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Editor information

Editors and Affiliations

  1. Equipe Combinatoire, CNRS, Paris, France

    Bruce A. Reed

  2. McGill University, Montreal, Canada

    Bruce A. Reed

  3. Departamento de Computacao—LIA, Universidade Federal do Ceara, Campus do Pici—Bloco 910, CEP 60455-760, Fortaleza, CE, Brasil

    Cláudia L. Sales

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Kohayakawa, Y., Rödl, V. (2003). Szemerédi’s Regularity Lemma and Quasi-randomness. In: Reed, B.A., Sales, C.L. (eds) Recent Advances in Algorithms and Combinatorics. CMS Books in Mathematics / Ouvrages de mathématiques de la SMC. Springer, New York, NY. https://doi.org/10.1007/0-387-22444-0_9

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  • DOI: https://doi.org/10.1007/0-387-22444-0_9

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