An Eulerian walk traverses each edge of a graph exactly once. What happens if you want to traverse each edge of a graph exactly twice? If you want to cover the graph with "double-running stitch", then you need to traverse each edge twice but also put conditions on how many edges you traverse in-between. Then you could add conditions on whether you traverse the edges once in each direction or twice in the same direction. Which graphs can you still traverse? Classical algorithms for solving mazes give us some answers to these questions, but others are still open.