Graph limits and parameter testing

Christian Borgs, Jennifer Chayes, L. Lovász, Vera T. Sós, Balázs Szegedy, Katalin Vesztergombi

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

95 Citations (Scopus)

Abstract

We define a distance of two graphs that reflects the closeness of both local and global properties, We also define convergence of a sequence of graphs, and show that a graph sequence is convergent if and only if it is Cauchy in this distance. Every convergent graph sequence has a limit in the form of a symmetric measurable function in two variables. We use these notions of distance and graph limits to give a general theory for parameter testing. As examples, we provide short proofs of the testability of MaxCut and the recent result of Alon and Shapira about the testability of hereditary graph properties.

Original languageEnglish
Title of host publicationProceedings of the Annual ACM Symposium on Theory of Computing
Pages261-270
Number of pages10
Volume2006
Publication statusPublished - 2006
Event38th Annual ACM Symposium on Theory of Computing, STOC'06 - Seattle, WA, United States
Duration: May 21 2006May 23 2006

Other

Other38th Annual ACM Symposium on Theory of Computing, STOC'06
CountryUnited States
CitySeattle, WA
Period5/21/065/23/06

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Keywords

  • Convergence of graphs
  • Distance of graphs
  • Graph homomorphism
  • Graph limit
  • Property testing

ASJC Scopus subject areas

  • Software

Cite this

Borgs, C., Chayes, J., Lovász, L., Sós, V. T., Szegedy, B., & Vesztergombi, K. (2006). Graph limits and parameter testing. In Proceedings of the Annual ACM Symposium on Theory of Computing (Vol. 2006, pp. 261-270)

Graph limits and parameter testing. / Borgs, Christian; Chayes, Jennifer; Lovász, L.; Sós, Vera T.; Szegedy, Balázs; Vesztergombi, Katalin.

Proceedings of the Annual ACM Symposium on Theory of Computing. Vol. 2006 2006. p. 261-270.

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

Borgs, C, Chayes, J, Lovász, L, Sós, VT, Szegedy, B & Vesztergombi, K 2006, Graph limits and parameter testing. in Proceedings of the Annual ACM Symposium on Theory of Computing. vol. 2006, pp. 261-270, 38th Annual ACM Symposium on Theory of Computing, STOC'06, Seattle, WA, United States, 5/21/06.
Borgs C, Chayes J, Lovász L, Sós VT, Szegedy B, Vesztergombi K. Graph limits and parameter testing. In Proceedings of the Annual ACM Symposium on Theory of Computing. Vol. 2006. 2006. p. 261-270
Borgs, Christian ; Chayes, Jennifer ; Lovász, L. ; Sós, Vera T. ; Szegedy, Balázs ; Vesztergombi, Katalin. / Graph limits and parameter testing. Proceedings of the Annual ACM Symposium on Theory of Computing. Vol. 2006 2006. pp. 261-270
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