Abstract: | The paper deals with panchromatic 3-colorings of random hypergraphs. A vertex 3-coloring is said to be panchromatic for a hypergraph if every color can be found on every edge. Let denote the binomial model of a random -uniform hypergraph on vertices. For given fixed , and , we prove that if then admits a panchromatic 3-coloring with probability tending to 1 as , but if is large enough and then does not admit a panchromatic 3-coloring with probability tending to 1 as . |