Before revision:  We prove that there exists a minimal splitting with respect to which a game is separable . Moreover we prove that in every strategic equivalence class, there is a game separable with respect to the minimal splitting in the class. This game is also graphical with respect to the smallest graph in the class, which represent a minimal complexity graphical description for the game.
After revision:  We prove that there exists a minimal splitting with respect to which a game is separable , providing a minimal complexity description for the game.