On the chromatic number of a random hypergraph

<p>We consider the problem of <em>k</em>-colouring a random <em>r</em>-uniform hypergraph with <em>n</em> vertices and <em>cn</em> edges, where <em>k</em>, <em>r</em>, <em>c </em> 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.