  A mixed hypergraph is a triple $H=(V,\mathcal{C},\mathcal{D})$, where $V$ is
a set of vertices, $\mathcal{C}$ and $\mathcal{D}$ are sets of hyperedges. A
vertex-coloring of $H$ is proper if $C$-edges are not totally multicolored and
$D$-edges are not monochromatic. The feasible set $S(H)$ of $H$ is the set of
all integers, $s$, such that $H$ has a proper coloring with $s$ colors.
  Bujt\'as and Tuza [Graphs and Combinatorics 24 (2008), 1--12] gave a
characterization of feasible sets for mixed hypergraphs with all $C$- and
$D$-edges of the same size $r$, $r\geq 3$.
  In this note, we give a short proof of a complete characterization of all
possible feasible sets for mixed hypergraphs with all $C$-edges of size $\ell$
and all $D$-edges of size $m$, where $\ell, m \geq 2$. Moreover, we show that
for every sequence $(r(s))_{s=\ell}^n$, $n \geq \ell$, of natural numbers there
exists such a hypergraph with exactly $r(s)$ proper colorings using $s$ colors,
$s = \ell,\ldots,n$, and no proper coloring with more than $n$ colors. Choosing
$\ell = m=r$ this answers a question of Bujt\'as and Tuza, and generalizes
their result with a shorter proof.
