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Questions about the branch of combinatorics called graph theory (not to be used for questions concerning the graph of a function). This tag can be further specialized via using it in combination with more specialized tags such as extremal-graph-theory, spectral-graph-theory, algebraic-graph-theory, topological-graph-theory, random-graphs, graph-colorings and several others.

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Enumerating all non-planar embeddings of a generic connected graph in the plane

As I mentioned in my comment, there are two kinds of problems here: If the graph is generically rigid, this is an enumeration problem, and quite a hard one. If the graph is generically flexible, the …
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