  Let $C_n^k$ be the $k$-th power of a cycle on $n$ vertices (i.e. the vertices
of $C_n^k$ are those of the $n$-cycle, and two vertices are connected by an
edge if their distance along the cycle is at most $k$). For each vertex draw
uniformly at random a subset of size $c$ from a base set $S$ of size $s=s(n)$.
In this paper we solve the problem of determining the asymptotic probability of
the existence of a proper colouring from the lists for all fixed values of
$c,k$, and growing $n$.
