  We introduce a game on graphs. By a theorem of Zermelo, each instance of the
game on a finite graph is determined. While the general decision problem on
which player has a winning strategy in a given instance of the game is
unsolved, we solve the decision problem for a specific class of finite graphs.
This result is then applied to a permutation sorting game to prove the
optimality of a proportional bound under which TWO has a winning strategy.
