 
Summary: Linear Equations, Arithmetic Progressions and Hypergraph
Property Testing
Noga Alon
Asaf Shapira
Abstract
For a fixed kuniform hypergraph D (kgraph for short, k 3), we say that a kgraph H
satisfies property PD (resp. P
D) if it contains no copy (resp. induced copy) of D. Our goal in
this paper is to classify the kgraphs D for which there are propertytesters for testing PD and
P
D whose query complexity is polynomial in 1/ . For such kgraphs we say that PD (resp. P
D)
is easily testable.
For P
D, we prove that aside from a single 3graph, P
D is easily testable if and only if D
is a single kedge. We further show that for large k, one can use more sophisticated techniques
in order to obtain better lower bounds for any large enough kgraph. These results extend and
improve previous results about graphs [5] and kgraphs [18].
For PD, we show that for any kpartite kgraph D, PD is easily testable, by giving an efficient
