The algorithmic aspects of the regularity lemma
Journal of Algorithms
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Testing graphs for colorable properties
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Measures on monotone properties of graphs
Discrete Applied Mathematics
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
Regular Languages are Testable with a Constant Number of Queries
SIAM Journal on Computing
SIAM Journal on Discrete Mathematics
Testing subgraphs in directed graphs
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Efficient Testing of Large Graphs
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Testing of function that have small width branching programs
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Journal of Algorithms
Testing Subgraphs in Large Graphs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Three theorems regarding testing graph properties
Random Structures & Algorithms
Functions that have read-twice constant width branching programs are not necessarily testable
Random Structures & Algorithms
Regularity lemma for k-uniform hypergraphs
Random Structures & Algorithms
Testing versus estimation of graph properties
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Additive Approximation for Edge-Deletion Problems
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
A Characterization of the (natural) Graph Properties Testable with One-Sided Error
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A combinatorial characterization of the testable graph properties: it's all about regularity
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Graph limits and parameter testing
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Property testing in hypergraphs and the removal lemma
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
On testable properties in bounded degree graphs
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Theoretical Computer Science
Property Testing: A Learning Theory Perspective
Foundations and Trends® in Machine Learning
Testing Fourier Dimensionality and Sparsity
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Strongly Chordal and Chordal Bipartite Graphs Are Sandwich Monotone
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Algorithmic and Analysis Techniques in Property Testing
Foundations and Trends® in Theoretical Computer Science
Playing to retain the advantage
Combinatorics, Probability and Computing
Property testing and parameter testing for permutations
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Lower bounds for testing triangle-freeness in Boolean functions
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Introduction to testing graph properties
Property testing
Introduction to testing graph properties
Property testing
Introduction to testing graph properties
Studies in complexity and cryptography
Contemplations on testing graph properties
Studies in complexity and cryptography
Strongly chordal and chordal bipartite graphs are sandwich monotone
Journal of Combinatorial Optimization
Additive approximation for edge-deletion problems
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Property testing and the branching program size of boolean functions
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
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A graph property is called monotone if it is closed under taking (not necessarily induced) subgraphs (or, equivalently, if it is closed under removal of edges and vertices). Many monotone graph properties are some of the most well-studied properties in graph theory, and the abstract family of all monotone graph properties was also extensively studied. Our main result in this paper is that any monotone graph property can be tested with one-sided error, and with query complexity depending only on ε. This result unifies several previous results in the area of property testing, and also implies the testability of well-studied graph properties that were previously not known to be testable. At the heart of the proof is an application of a variant of Szemerédi's Regularity Lemma. The main ideas behind this application may be useful in characterizing all testable graph properties, and in generally studying graph property testing.As a byproduct of our techniques we also obtain additional results in graph theory and property testing, which are of independent interest. One of these results is that the query complexity of testing testable graph properties with one-sided error may be arbitrarily large. Another result, which significantly extends previous results in extremal graph-theory, is that for any monotone graph property P, any graph that is ε -far from satisfying P, contains a subgraph of size depending on ε only, which does not satisfy P. Finally, we prove the following compactness statement: If a graph G is ε-far from satisfying a (possibly infinite) set of graph properties P, then it is at least δ P ε-far from satisfying one of the properties.