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Algorithmic Aspects of Regularity

  • Y. Kohayakawa
  • V. Rödl
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1776)

Abstract

Szemerédi’s celebrated regularity lemma proved to be a fundamental result in graph theory. Roughly speaking, his lemma states that any graph may be approximated by a union of a bounded number of bipartite graphs, each of which is ‘pseudorandom’. As later proved by Alon, Duke, Lefmann, Rödl, and Yuster, there is a fast deterministic algorithm for finding such an approximation, and therefore many of the existential results based on the regularity lemma could be turned into constructive results. In this survey, we discuss some recent developments concerning the algorithmic aspects of the regularity lemma.

Keywords

Bipartite Graph Input Graph Algorithmic Version Graph Property Dense Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Y. Kohayakawa
    • 1
  • V. Rödl
    • 2
  1. 1.Instituto de Matemática e EstatísticaUniversidade de São PauloSão PauloBrazil
  2. 2.Department of Mathematics and Computer ScienceEmory UniversityAtlantaUSA

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