  A $k$-subcoloring of a graph is a partition of the vertex set into at most
$k$ cluster graphs, that is, graphs with no induced $P_3$. 2-subcoloring is
known to be NP-complete for comparability graphs and three subclasses of planar
graphs, namely triangle-free planar graphs with maximum degree 4, planar
perfect graphs with maximum degree 4, and planar graphs with girth 5. We show
that 2-subcoloring is also NP-complete for planar comparability graphs with
maximum degree 4.
