A note on rainbow-free colorings of uniform hypergraphs.

A rainbow-free coloring of a k -uniform hypergraph H is a vertex-coloring which uses k colors but with the property that no edge of H attains all colors. Koerkamp and Z̆ivný showed that p = (k − 1) (log n) / n is the threshold function for the existence of a rainbow-free coloring of the random k -uniform hypergraph G k (n , p) , and presented that the case when p is close to the threshold is open. In this paper, we give an answer to the question. [ABSTRACT FROM AUTHOR]