Testing hypergraph colorability

We study the problem of testing properties of hypergraphs. The goal of property testing is to distinguish between the case whether a given object has a certain property or is “far away” from the property. We prove that the fundamental problem of ℓ-colorability of k-uniform hypergraphs can be tested in time independent of the size of the hypergraph. We present a testing algorithm that examines only (kℓ/ε)O(k) entries of the adjacency matrix of the input hypergraph, where ε is a distance parameter independent of the size of the hypergraph. The algorithm tests only a constant number of entries in the adjacency matrix provided that ℓ, k, and ε are constants. This result is a generalization of previous results about testing graph colorability.