Israel Journal of Mathematics

, Volume 178, Issue 1, pp 113-156

First online:

Testing properties of graphs and functions

  • László LovászAffiliated withInstitute of Mathematics, Eötvös Loránd University Email author 
  • , Balázs SzegedyAffiliated with

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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.