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 H(n,k,p) denote the binomial model of a random k-uniform hypergraph on n vertices. For given fixed c>0, k⩾3 and p=cn∕nk, we prove that if c<ln33⋅32k−ln32−O32kthen H(n,k,p) admits a panchromatic 3-coloring with probability tending to 1 as n→∞, but if k is large enough and c>ln33⋅32k−ln32+O34kthen H(n,k,p) does not admit a panchromatic 3-coloring with probability tending to 1 as n→∞.
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