  A 2-coloring of a hypergraph is a mapping from its vertices to a set of two
colors such that no edge is monochromatic. Let $H_k(n,m)$ be a random
$k$-uniform hypergraph on $n$ vertices formed by picking $m$ edges uniformly,
independently and with replacement. It is easy to show that if $r \geq r_c =
2^{k-1} \ln 2 - (\ln 2) /2$, then with high probability $H_k(n,m=rn)$ is not
2-colorable. We complement this observation by proving that if $r \leq r_c - 1$
then with high probability $H_k(n,m=rn)$ is 2-colorable.
