A separator theorem for graphs with an excluded minor and its applications
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
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)
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
Graph minors. XVI. excluding a non-planar graph
Journal of Combinatorial Theory Series B
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
Parameterized graph separation problems
Theoretical Computer Science - Parameterized and exact computation
A Combinatorial Characterization of the Testable Graph Properties: It's All About Regularity
SIAM Journal on Computing
Local Graph Partitions for Approximation and Testing
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
A Separator Theorem in Minor-Closed Classes
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Property testing: current research and surveys
Property testing: current research and surveys
Finding topological subgraphs is fixed-parameter tractable
Proceedings of the forty-third annual ACM symposium on Theory of computing
Every property of hyperfinite graphs is testable
Proceedings of the forty-third annual ACM symposium on Theory of computing
Property Testing on k-Vertex-Connectivity of Graphs
Algorithmica
Constant-time algorithms for sparsity matroids
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
On the excluded minor structure theorem for graphs of large tree-width
Journal of Combinatorial Theory Series B
Complete graph minors and the graph minor structure theorem
Journal of Combinatorial Theory Series B
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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 2/3, say) between the case that G satisfies P and the case that one should add/remove at least ε dn edges of $G$ to make it satisfy P. In sharp contrast to property testing of dense graphs, which is relatively well understood, only few properties are known to be testable with a constant number of queries in the bounded-degree model. In particular, no global monotone (i.e,~closed under edge deletions) property that expander graphs can satisfy has been shown to be testable in constant time so far. In this paper, we identify for the first time a natural family of global monotone property that expander graphs can satisfy and can be efficiently tested in the bounded degree model. Specifically, we show that, for any integer t ≥ 1, Kt-subdivision-freeness is testable with a constant number of queries in the bounded-degree model. This property was not previously known to be testable even with o(n) queries. Note that an expander graph with all degree less than t-1 does not have a Kt-subdivision. The proof is based on a novel combination of some results that develop the framework of partitioning oracles, together with structural graph theory results that develop the seminal graph minor theory by Robertson and Seymour. As far as we aware, this is the first result that bridges property testing and structural graph theory. Although we know a rough structure for graphs without H-minors from the famous graph minor theory by Robertson and Seymour, there is no corresponding structure theorem for graphs without H-subdivisions so far, even K5-subdivision-free graphs. Therefore, subdivisions and minors are very different in a graph structural sense.