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.

翻译：我们用一个未定向且未加权的图表来研究最大 K- cut 游戏, 以便找出最佳解决方案是否也是强烈的平衡。 虽然我们没有证明, 通过证明计算切分差的替代公式, 以获得强烈偏差, 我们证明最佳的解决方案是 7 个稳定的平衡。 此外, 我们证明, 与强烈偏差相比, 最小子集的一些特性, 表明每个节点会偏离其邻居的颜色, 而这些节点会诱发连接子集 。