Gabriel Nivasch’s “multi-stack” algorithm identifies these structures. An unsolved problem that asks whether these structures produce a double cover reduces to asking about “snarks.” These structures cause Kahn’s algorithm to output an empty list, since they prevent topological sortings. Pollard’s algorithm for integer factorization is named for the eventual resemblance to one of these structures over time. Gosper’s algorithm for detecting these structures improves upon another algorithm that creates a leading and trailing pointer called a “hare” and “tortoise” and is named (10[1])for Floyd. Detecting these structures by checking already-visited nodes (-5[1])ensures that (-5[1])DFS halts. The [emphasize] absence of these structures defines the “A” in a DAG. For 10 points, name (10[2])these paths in a graph that (-5[1])eventually lead back to their start. (10[3])■END■