  We study the max k-cut game on an undirected and unweighted graph in order to
find out whether an optimal solution is also a strong equilibrium. While we do
fail to show that, by proving an alternate formula for computing the cut value
difference for a strong deviation, we show that optimal solutions are 7-stable
equilibria.
  Furthermore, we prove some properties of minimal subsets with respect to a
strong deviation, showing that each of their nodes will deviate towards the
color of one of their neighbors and that those subsets induce connected
subgraphs.
