Quasi-randomness and algorithmic regularity for graphs with general degree distributions

Noga Alon, Amin Coja-Oghlan, Hiêp Hàn, Mihyun Kang, Vojtěch Rödl, Mathias Schacht

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

We deal with two very related subjects: quasi-randomness and regular partitions. The purpose of the concept of quasi-randomness is to measure how much a given graph "resembles" a random one. Moreover, a regular partition approximates a given graph by a bounded number of quasi-random graphs. Regarding quasi-randomness, we present a new spectral characterization of low discrepancy, which extends to sparse graphs. Concerning regular partitions, we present a novel concept of regularity that takes into account the graph's degree distribution, and show that if G = (V, E) satisfies a certain boundedness condition, then G admits a regular partition. In addition, building on the work of Alon and Naor [4], we provide an algorithm that computes a regular partition of a given (possibly sparse) graph G in polynomial time.

Original languageEnglish (US)
Title of host publicationAutomata, Languages and Programming - 34th International Colloquium, ICALP 2007, Proceedings
PublisherSpringer Verlag
Pages789-800
Number of pages12
ISBN (Print)3540734198, 9783540734192
DOIs
StatePublished - 2007
Externally publishedYes
Event34th International Colloquium on Automata, Languages and Programming, ICALP 2007 - Wroclaw, Poland
Duration: Jul 9 2007Jul 13 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4596 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other34th International Colloquium on Automata, Languages and Programming, ICALP 2007
CountryPoland
CityWroclaw
Period7/9/077/13/07

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Keywords

  • Grothendieck's inequality
  • Laplacian eigenvalues
  • Quasi-random graphs
  • Regularity lemma
  • Sparse graphs

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  • Cite this

    Alon, N., Coja-Oghlan, A., Hàn, H., Kang, M., Rödl, V., & Schacht, M. (2007). Quasi-randomness and algorithmic regularity for graphs with general degree distributions. In Automata, Languages and Programming - 34th International Colloquium, ICALP 2007, Proceedings (pp. 789-800). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4596 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-540-73420-8_68