In the context of full words, the minimal cardinality of unavoidable sets of words of a given length
*m* over a *k*-letter alphabet has been shown to be precisely equal to *c(m,k)*,
the number of conjugacy classes of words of that length over the given alphabet. We examine the case of
partial words of length *m* with *h* holes over a *k*-letter alphabet and attempt
to find bounds for the minimal cardinality of such unavoidable sets.

*Keywords:* Combinatorics on words; Partial words; Unavoidable sets.