  A proper coloring of a graph is \emph{proper conflict-free} if every
non-isolated vertex $v$ has a neighbor whose color is unique in the
neighborhood of $v$. A proper coloring of a graph is \emph{odd} if for every
non-isolated vertex $v$, there is a color appearing an odd number of times in
the neighborhood of $v$. For an integer $k$, the \textsc{PCF $k$-Coloring}
problem asks whether an input graph admits a proper conflict-free $k$-coloring
and the \textsc{Odd $k$-Coloring} asks whether an input graph admits an odd
$k$-coloring. We show that for every integer $k\geq3$, both problems are
NP-complete, even if the input graph is bipartite. Furthermore, we show that
the \textsc{PCF $4$-Coloring} problem is NP-complete when the input graph is
planar.
