Some 3CNF properties are hard to test
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Testing subgraphs in directed graphs
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Robust pcps of proximity, shorter pcps and applications to coding
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Approximate max-integral-flow/min-multicut theorems
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Testing subgraphs in directed graphs
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A large lower bound on the query complexity of a simple boolean function
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A Characterization of Easily Testable Induced Subgraphs
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On testable properties in bounded degree graphs
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Comparing the strength of query types in property testing: the case of testing k-colorability
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Every minor-closed property of sparse graphs is testable
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Algebraic property testing: the role of invariance
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Testing monotonicity over graph products
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Property testing
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Property testing
Sublinear graph approximation algorithms
Property testing
Hierarchy theorems for property testing
Property testing
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Contemplations on testing graph properties
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Characterizations of locally testable linear-and affine-invariant families
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Characterizations of locally testable linear- and affine-invariant families
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A lower bound for distribution-free monotonicity testing
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We consider the problem of testing 3-colorability in the bounded-degree model.We show that, for small enough \varepsilon, every tester for 3-colorability must have query complexity \Omega \text{(n)}. This is the first linear lower bound for testing a natural graph property in the bounded-degree model. An \Omega (\sqrt n ) lower bound was previously known.For one-sided error testers, we also show an \Omega \text{(n)} lower bound for testers that distinguish 3-colorable graphs from graphs that are({\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 3}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$3$}} - \alpha )- far from 3-colorable, for arbitrarily small \alpha. In contrast a polynomial time algorithm by Frieze and Jerrum distinguishes 3-colorable graphs from graphs that are {1 \mathord{\left/{\vphantom {1 5}} \right.\kern-\nulldelimiterspace} 5}-far from 3-colorable.As a by-product of our techniques, we obtain tight unconditional lower bounds on the approximation ratios achievable by sublinear time algorithms for Max E3SAT, Max E3LIN-2 and other problems.