  A set of colored graphs are compatible, if for every color $i$, the number of
vertices of color $i$ is the same in every graph. A simultaneous embedding of
$k$ compatibly colored graphs, each with $n$ vertices, consists of $k$ planar
polyline drawings of these graphs such that the vertices of the same color are
mapped to a common set of vertex locations.
  We prove that simultaneous embedding of $k\in o(\log \log n)$ colored planar
graphs, each with $n$ vertices, can always be computed with a sublinear number
of bends per edge. Specifically, we show an $O(\min\{c, n^{1-1/\gamma}\})$
upper bound on the number of bends per edge, where $\gamma = 2^{\lceil k/2
\rceil}$ and $c$ is the total number of colors. Our bound, which results from a
better analysis of a previously known algorithm [Durocher and Mondal, SIAM J.
Discrete Math., 32(4), 2018], improves the bound for $k$, as well as the bend
complexity by a factor of $\sqrt{2}^{k}$. The algorithm can be generalized to
obtain small universal point sets for colored graphs. We prove that $n\lceil
c/b \rceil$ vertex locations, where $b\ge 1$, suffice to embed any set of
compatibly colored $n$-vertex planar graphs with bend complexity $O(b)$, where
$c$ is the number of colors.
