  Given an edge-weighted graph $G$ with a set $Q$ of $k$ terminals, a mimicking
network is a graph with the same set of terminals that exactly preserves the
sizes of minimum cuts between any partition of the terminals. A natural
question in the area of graph compression is to provide as small mimicking
networks as possible for input graph $G$ being either an arbitrary graph or
coming from a specific graph class.
  In this note we show an exponential lower bound for cut mimicking networks in
planar graphs: there are edge-weighted planar graphs with $k$ terminals that
require $2^{k-2}$ edges in any mimicking network. This nearly matches an upper
bound of $O(k 2^{2k})$ of Krauthgamer and Rika [SODA 2013, arXiv:1702.05951]
and is in sharp contrast with the $O(k^2)$ upper bound under the assumption
that all terminals lie on a single face [Goranci, Henzinger, Peng,
arXiv:1702.01136]. As a side result we show a hard instance for the
double-exponential upper bounds given by Hagerup, Katajainen, Nishimura, and
Ragde~[JCSS 1998], Khan and Raghavendra~[IPL 2014], and Chambers and
Eppstein~[JGAA 2013].
