  We study rainbow-free colourings of $k$-uniform hypergraphs; that is,
colourings that use $k$ colours but with the property that no hyperedge attains
all colours. We show that $p^*=(k-1)(\ln n)/n$ is the threshold function for
the existence of a rainbow-free colouring in a random $k$-uniform hypergraph.

Combinatorics;Discrete Mathematics