  There are many applications of max flow with capacities that depend on one or
more parameters. Many of these applications fall into the "Source-Sink
Monotone" framework, a special case of Topkis's monotonic optimization
framework, which implies that the parametric min cuts are nested. When there is
a single parameter, this property implies that the number of distinct min cuts
is linear in the number of nodes, which is quite useful for constructing
algorithms to identify all possible min cuts.
  When there are multiple Source-Sink Monotone parameters and the vector of
parameters are ordered in the usual vector sense, the resulting min cuts are
still nested. However, the number of distinct min cuts was an open question. We
show that even with only two parameters, the number of distinct min cuts can be
exponential in the number of nodes.
