  For an $r$-uniform hypergraph $H$, let $f(H)$ be the minimum number of
complete $r$-partite $r$-uniform subhypergraphs of $H$ whose edge sets
partition the edge set of $H$. For a graph $G$, $f(G)$ is the bipartition
number of $G$ which was introduced by Graham and Pollak in 1971. In 1988,
Erd\H{o}s conjectured that if $G \in G(n,1/2)$, then with high probability
$f(G)=n-\alpha(G)$, where $\alpha(G)$ is the independence number of $G$. This
conjecture and related problems have received a lot of attention recently. In
this paper, we study the value of $f(H)$ for a typical $r$-uniform hypergraph
$H$. More precisely, we prove that if $(\log n)^{2.001}/n \leq p \leq 1/2$ and
$H \in H^{(r)}(n,p)$, then with high probability
$f(H)=(1-\pi(K^{(r-1)}_r)+o(1))\binom{n}{r-1}$, where $\pi(K^{(r-1)}_r)$ is the
Tur\'an density of $K^{(r-1)}_r$.
