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Given: A degree sequence.

Wanted: A graph and a polyhedral embedding of this graph (described by a rotation system or something equivalent). By polyhedral embedding I mean only the combinatorial concept. See here.

Is there a fast way to do this? I tried a backtracking approach, adding edges one at a time, but it is too slow. It becomes intractable for a 3-regular graph of 30 vertices.

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