Israel Journal of Mathematics

, Volume 178, Issue 1, pp 113–156

Testing properties of graphs and functions

Article

Abstract

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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Hebrew University Magnes Press 2010

Authors and Affiliations

  1. 1.Institute of MathematicsEötvös Loránd UniversityBudapestHungary
  2. 2.TorontoCanada

Personalised recommendations