Planarity as a game

In the on-line solitaire game Planarity, the player is given an undirected planar graph -- vertices displayed as dots, edges as lines -- but presented in a form with crossings. The player can use the mouse to drag the vertices around in the window, one by one. The object of the game is to eliminate all of the crossings. To claim victory, the player clicks on a button; the game checks to make sure that there are no crossings and then sets up a new graph, with more vertices and edges.