Every Minor-Closed Property of Sparse Graphs is Testable

13 years 4 months ago

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Testing a property P of graphs in the bounded degree model is the following computational 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 dn edges of G to make it satisfy P. 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 establish that planarity is testable in the bounded degree model, thus answering an open problem raised by Goldreich and Ron [STOC 1997] in the paper that introduced this model of property testing. We further establish the testability of other well studied graph properties like being pouter-planar, series-parallel, bounded genus, bounded tree-width and several others. None of these properties was previously known to be test...

Itai Benjamini, Oded Schramm, Asaf Shapira

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