Testing Hypergraph Coloring

In this paper we initiate the study 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 (k l/Ɛ)(ċk) entries of the adjacency matrix of the input hypergraph, where Ɛ is a distance parameter independent of the size of the hypergraph. Notice that this algorithm tests only a constant number of entries in the adjacency matrix provided that l, k, and Ɛ are constant.

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