ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Local graph exploration and fast property testing
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Testing expansion in bounded-degree graphs
Combinatorics, Probability and Computing
Local Monotonicity Reconstruction
SIAM Journal on Computing
Property testing
Property testing
Local property reconstruction and monotonicity
Property testing
Property testing
Property testing
Local property reconstruction and monotonicity
Property testing
Testing permutation properties through subpermutations
Theoretical Computer Science
Inflatable graph properties and natural property tests
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Testing Eulerianity and connectivity in directed sparse graphs
Theoretical Computer Science
An Expansion Tester for Bounded Degree Graphs
SIAM Journal on Computing
Testing Fourier Dimensionality and Sparsity
SIAM Journal on Computing
Testing Symmetric Properties of Distributions
SIAM Journal on Computing
SIAM Journal on Discrete Mathematics
A note on permutation regularity
Discrete Applied Mathematics
Property testing in sparse directed graphs: strong connectivity and subgraph-freeness
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Testing subdivision-freeness: property testing meets structural graph theory
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Testing linear-invariant function isomorphism
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Proceedings of the 5th conference on Innovations in theoretical computer science
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A common thread in all of the recent results concerning the testing of dense graphs is the use of Szemerédi's regularity lemma. In this paper we show that in some sense this is not a coincidence. Our first result is that the property defined by having any given Szemerédi-partition is testable with a constant number of queries. Our second and main result is a purely combinatorial characterization of the graph properties that are testable with a constant number of queries. This characterization (roughly) says that a graph property ${\cal P}$ can be tested with a constant number of queries if and only if testing ${\cal P}$ can be reduced to testing the property of satisfying one of finitely many Szemerédi-partitions. This means that in some sense, testing for Szemerédi-partitions is as hard as testing any testable graph property. We thus resolve one of the main open problems in the area of property-testing, which was first raised by Goldreich, Goldwasser, and Ron [J. ACM, 45 (1998), pp. 653-750] in the paper that initiated the study of graph property-testing. This characterization also gives an intuitive explanation as to what makes a graph property testable.