  Let $\Omega_q=\Omega_q(H)$ denote the set of proper $[q]$-colorings of the
hypergraph $H$. Let $\Gamma_q$ be the graph with vertex set $\Omega_q$ and an
edge ${\sigma,\tau\}$ where $\sigma,\tau$ are colorings iff $h(\sigma,\tau)=1$.
Here $h(\sigma,\tau)$ is the Hamming distance $|\{v\in
V(H):\sigma(v)\neq\tau(v)\}|$. We show that if $H=H_{n,m;k},\,k\geq 2$, the
random $k$-uniform hypergraph with $V=[n]$ and $m=dn/k$ then w.h.p. $\Gamma_q$
is connected if $d$ is sufficiently large and $q\gtrsim (d/\log d)^{1/(k-1)}$.
