Removal lemmas with polynomial bounds

Lior Gishboliner, Asaf Shapira

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We give new sufficient and necessary criteria guaranteeing that a hereditary graph property can be tested with a polynomial query complexity. Although both are simple combinatorial criteria, they imply almost all prior positive and negative results of this type, as well as many new ones. One striking application of our results is that every semi-algebraic graph property (e.g., being an interval graph, a unit-disc graph etc.) can be tested with a polynomial query complexity. This confirms a conjecture of Alon. The proofs combine probabilistic ideas together with a novel application of a conditional regularity lemma for matrices, due to Alon, Fischer and Newman.

Original languageEnglish
Title of host publicationSTOC 2017 - Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing
EditorsPierre McKenzie, Valerie King, Hamed Hatami
Pages510-522
Number of pages13
ISBN (Electronic)9781450345286
DOIs
StatePublished - 19 Jun 2017
Event49th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2017 - Montreal, Canada
Duration: 19 Jun 201723 Jun 2017

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
VolumePart F128415

Conference

Conference49th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2017
Country/TerritoryCanada
CityMontreal
Period19/06/1723/06/17

Keywords

  • Graph property testing
  • Removal lemma

All Science Journal Classification (ASJC) codes

  • Software

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