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.
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Kohayakawa, Y., Rödl, V. (2000). Algorithmic Aspects of Regularity. In: Gonnet, G.H., Viola, A. (eds) LATIN 2000: Theoretical Informatics. LATIN 2000. Lecture Notes in Computer Science, vol 1776. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10719839_1
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DOI: https://doi.org/10.1007/10719839_1
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