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Euler circuit in a directed multigraph
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[QUOTE="andrewkirk, post: 5502474, member: 265790"] I don't think you are interpreting the question quite correctly. You are reading it as something like: Whereas I think what it is saying is: So you are asked to prove that: $$DirectedMultiGraph(G)\wedge NoIsolatedVertices(G)\wedge (NumEulerCircuits(G)\geq 1) \leftrightarrow DirectedMultiGraph(G)\wedge NoIsolatedVertices(G)\wedge WeaklyConnected(G)\wedge (\forall v\in V(G):\ InDegree(v)=OutDegree(v))$$ Also, if you can prove StronglyConnected then you have also proven WeaklyConnected since the former entails the latter (but not vice versa). The usual convention in mathematics is that Weakly-X or Partially-X is entailed by Strongly-X, Totally-X or just plain X, but not vice versa. [/QUOTE]
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Euler circuit in a directed multigraph
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