Testing hypergraph coloring

Abstract

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 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 adjacency matrix of the input hypergraph, where 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 , k, and are constant. © 2011 Springer-Verlag Berlin Heidelberg.