Quasi-randomness is determined by the distribution of copies of a fixed graph in equicardinal large sets

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Abstract

For every fixed graph H and every fixed 0 < α < 1, we show that if a graph G has the property that all subsets of size αn contain the "correct" number of copies of H one would expect to find in the random graph G(n,p) then G behaves like the random graph G(n,p); that is, it is p-quasi-random in the sense of Chung, Graham, and Wilson [4].This solves a conjecture raised by Shapira [8] and solves in a strong sense an open problem of Simonovits and Sós [9].

Original languageEnglish
Title of host publicationApproximation, Randomization and Combinatorial Optimization
Subtitle of host publicationAlgorithms and Techniques - 11th International Workshop, APPROX 2008 and 12th International Workshop, RANDOM 2008, Proceedings
Pages596-601
Number of pages6
DOIs
StatePublished - 2008
Event11th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2008 and 12th International Workshop on Randomization and Computation, RANDOM 2008 - Boston, MA, United States
Duration: 25 Aug 200827 Aug 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5171 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference11th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2008 and 12th International Workshop on Randomization and Computation, RANDOM 2008
Country/TerritoryUnited States
CityBoston, MA
Period25/08/0827/08/08

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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