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.
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