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https://mathworld.wolfram.com/EulerianGraph.html

  1. Euler showed (without proof) that a connected simple graph is Eulerian iff it has no graph vertices of odd degree (i.e., all vertices are of even degree). Euler showed (without proof) that a connected simple graph is Eulerian iff it has no graph vertices of odd degree (i.e., all vertices are of even degree). 

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