  A partition $\pi=\{V_{1},V_{2},...,V_{k}\}$ of the vertex set $V$ of a graph
$G$ into $k$ color classes $V_{i}$, with $1\leq i\leq k$ is called a quorum
coloring of $G$ if for every vertex $v\in V$, at least half of the vertices in
the closed neighborhood $N[v]$ of $v$ have the same color as $v$. The maximum
cardinality of a quorum coloring of $G$ is called the quorum coloring number of
$G$ and is denoted by $\psi_{q}(G)$. A quorum coloring of order $\psi_{q}(G)$
is a $\psi_{q}$-coloring. The determination of the quorum coloring number or
design a linear-time algorithm computing it in a perfect $N$-ary tree has been
posed recently as an open problem by Sahbi. In this paper, we answer this
problem by designing a linear-time algorithm for finding both a
$\psi_{q}$-coloring and the quorum coloring number for every perfect tree whose
the vertices at the same depth have the same degree.
