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ECCC
2008

Every Minor-Closed Property of Sparse Graphs is Testable

9 years 4 months ago
Every Minor-Closed Property of Sparse Graphs is Testable
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
Added 10 Dec 2010
Updated 10 Dec 2010
Type Journal
Year 2008
Where ECCC
Authors Itai Benjamini, Oded Schramm, Asaf Shapira
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