Testing properties of graphs and functions

Ĺaszĺo Lovász, Balázs Szegedy

Research output: Contribution to journalArticle

33 Citations (Scopus)


We define an analytic version of the graph property testing problem, which can be formulated as studying an unknown 2-variable symmetric function through sampling from its domain and studying the random graph obtained when using the function values as edge probabilities. We give a characterization of properties testable this way, and extend a number of results about "large graphs" to this setting. These results can be applied to the original graph-theoretic property testing. In particular, we give a new combinatorial characterization of the testable graph properties. Furthermore, we define a class of graph properties (flexible properties) which contains all the hereditary properties, and generalize various results of Alon, Shapira, Fischer, Newman and Stav from hereditary to flexible properties.

Original languageEnglish
Pages (from-to)113-156
Number of pages44
JournalIsrael Journal of Mathematics
Issue number1
Publication statusPublished - Dec 1 2010

ASJC Scopus subject areas

  • Mathematics(all)

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