  A graph $G$ is free $(a,b)$-choosable if for any vertex $v$ with $b$ colors
assigned and for any list of colors of size $a$ associated with each vertex
$u\ne v$, the coloring can be completed by choosing for $u$ a subset of $b$
colors such that adjacent vertices are colored with disjoint color sets. In
this note, a necessary and sufficient condition for a cycle to be free
$(a,b)$-choosable is given. As a corollary, some choosability results are
derived for graphs in which cycles are connected by a tree structure.
