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 -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 (k / )O(k) entries of the adjacencymatrix of the input hypergraph,where 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 , k, and are constants. This result is a generalization of previous results about testing graph colorability. © 2004 Elsevier B.V. All rights reserved.