Geometry and Generation of a New Graph Planarity Game

We introduce a new abstract graph game, SWAP PLANARITY, where the goal is to reach a state without edge intersections and a move consists of swapping the locations of two vertices connected by an edge. We analyze this puzzle game using concepts from graph theory and graph drawing, computational geometry, and complexity. Furthermore, we specify what good levels look like and we show how they can be generated. We also report on experiments that show how well the generation works.