5 research outputs found
Testing Hereditary Properties of Sequences
A hereditary property of a sequence is one that is preserved when restricting to subsequences. We show that there exist hereditary properties of sequences that cannot be tested with sublinear queries, resolving an open question posed by Newman et al. This proof relies crucially on an infinite alphabet, however; for finite alphabets, we observe that any hereditary property can be tested with a constant number of queries
Every Minor-Closed Property of Sparse Graphs is Testable
Suppose is a graph with degrees bounded by , and one needs to remove
more than of its edges in order to make it planar. We show that in
this case the statistics of local neighborhoods around vertices of is far
from the statistics of local neighborhoods around vertices of any planar graph
with the same degree bound. In fact, a similar result is proved for any
minor-closed property of bounded degree graphs.
As an immediate corollary of the above result 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, where the constant may depend on and , but not
on the graph size. None of these properties was previously known to be testable
even with queries