Because certain positions in Dots and Boxes reduce to Kayles positions, it is helpful to understand Kayles in order to analyze a generic Dots and Boxes position. Under normal play, Kayles can be solved in polynomial time using the Sprague-Grundy theory. "Node Kayles" is a generalization of Kayles to graphs in which each bowl “knocks down” (removes) a desired vertex and all its neighboring vertices. (Alternatively, this game can be viewed as two players finding an independent set together.) Schaefer (1978) proved that deciding the outcome of this game is PSPACE-complete. The same result holds for a partisan version of node Kayles, in which, for every node, only one of the players is allowed to choose that particular node as the knock down target.