Self-testing/correcting with applications to numerical problems
Journal of Computer and System Sciences - Special issue: papers from the 22nd ACM symposium on the theory of computing, May 14–16, 1990
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Journal of the ACM (JACM)
The extremal function for complete minors
Journal of Combinatorial Theory Series B
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
Testing the diameter of graphs
Random Structures & Algorithms
A Lower Bound for Testing 3-Colorability in Bounded-Degree Graphs
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
The Complexity of Learning Minor Closed Graph Classes
ALT '95 Proceedings of the 6th International Conference on Algorithmic Learning Theory
Three theorems regarding testing graph properties
Random Structures & Algorithms
Graph Minors. XX. Wagner's conjecture
Journal of Combinatorial Theory Series B - Special issue dedicated to professor W. T. Tutte
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
Algorithmic Graph Minor Theory: Decomposition, Approximation, and Coloring
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
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
On testable properties in bounded degree graphs
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Testing Expansion in Bounded-Degree Graphs
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
A separation theorem in property testing
Combinatorica
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
Parameterized Complexity
On proximity oblivious testing
Proceedings of the forty-first annual ACM symposium on Theory of computing
Towards a Study of Low-Complexity Graphs
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Hierarchy Theorems for Property Testing
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Algorithmic and Analysis Techniques in Property Testing
Foundations and Trends® in Theoretical Computer Science
Parameter testing in bounded degree graphs of subexponential growth
Random Structures & Algorithms
Testing outerplanarity of bounded degree graphs
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
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
The program of the mini-workshop
Property testing
Property testing
Introduction to testing graph properties
Property testing
Sublinear graph approximation algorithms
Property testing
Hierarchy theorems for property testing
Property testing
Property testing
The program of the mini-workshop
Property testing
Property testing
Introduction to testing graph properties
Property testing
Sublinear graph approximation algorithms
Property testing
Hierarchy theorems for property testing
Property testing
Property testing
Every property of hyperfinite graphs is testable
Proceedings of the forty-third annual ACM symposium on Theory of computing
Introduction to testing graph properties
Studies in complexity and cryptography
An efficient partitioning oracle for bounded-treewidth graphs
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
On Proximity-Oblivious Testing
SIAM Journal on Computing
A near-optimal sublinear-time algorithm for approximating the minimum vertex cover size
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
SIAM Journal on Discrete Mathematics
Property testing in sparse directed graphs: strong connectivity and subgraph-freeness
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Left and right convergence of graphs with bounded degree
Random Structures & Algorithms
A quasi-polynomial time partition oracle for graphs with an excluded minor
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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Testing a property P of graphs in the bounded degree model deals with the following problem: given a graph G of bounded degree d we should distinguish (with probability 0.9, say) between the case that G satisfies P and the case that one should add/remove at least ε d n edges of G to make it satisfy P. In sharp contrast to property testing of dense graphs, which is relatively well understood, very few properties are known to be testable in bounded degree graphs with a constant number of queries. In this paper we identify for the first time a large (and natural) family of properties that can be efficiently tested in bounded degree graphs, by showing that every minor-closed graph property can be tested with a constant number of queries. As a special case, we infer that many well studied graph properties, like being planar, outer-planar, series-parallel, bounded genus, bounded tree-width and several others, are testable with a constant number of queries. None of these properties was previously known to be testable even with o(n) queries. The proof combines results from the theory of graph minors with results on convergent sequences of sparse graphs, which rely on martingale arguments.