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For each segment extract the two endpoints (remembering which segment they came from), now sort the endpoints by (say) lexicographical ordering. Any two endpoints that are the same are now adjacent. so, scan the sorted list, attache adjacent segments that share endpoints, and then read the cycle by following the resulting list like structure among the ...


For a directed tree, it is possible to find an embeeding in a n-dimensional space, where n is the maximum branching factor of the tree. This approach could be also generalized for (rooted) DAGs. More to come in the forthcoming paper:

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