On the Chromatic Numbers of Random Hypergraphs

The asymptotic behavior of the chromatic number of the binomial random hypergraph H(n,k,p) is studied in the case when k ⩾ 4 is fixed, n tends to infinity, and p = p ( n ) is a function. If p = p ( n ) does not decrease too slowly, we prove that the chromatic number of H(n,k,p) is concentrated in two or three consecutive values, which can be found explicitly as functions of n , p , and k .