Bounds for threshold probabilities for fractional colorability properties of random hypergraphs

The paper deals with the well-known problem concerning the threshold probabilities for coloring properties of random hypergraphs. We consider the binomial model of a random k-uniform hypergraph H(n, k, p) in the sparse regime, when the expected number of edges is a linear function of the number of vertices. As the main result we obtain the estimates of the sharp threshold probability for the property of proper (5 : 2)-fractional colorability of H(n, k, p).