On the chromatic number of a random hypergraph

We consider the problem of k-colouring a random r-uniform hypergraph with n vertices and cn edges, where k, r, c remain constant as n→∞. Achlioptas and Naor showed that the chromatic number of a random graph in this setting, the case r=2, must have one of two easily computable values as n→∞. We give a complete generalisation of this result to random uniform hypergraphs.