  We give an example of a cluster-tilted algebra A with quiver Q, such that the
associated cluster algebra has a denominator vector which is not the dimension
vector of any indecomposable A-module. This answers a question posed by T.
Nakanishi. The relevant example is a cluster-tilted algebra associated with a
tame hereditary algebra. We show that for such a cluster-tilted algebra A, we
can write any denominator vector as a sum of the dimension vectors of at most
three indecomposable rigid A-modules. In order to do this it is necessary, and
of independent interest, to first classify the indecomposable rigid A-modules
in this case.
