(idea) by Gaff Thu Jan 18 2001 at 0:40:46
Theorem
A graph is Eulerian (i.e. a Euler tour is possible) if and only if all its vertices have even degree. That is at each point, the number of edges going into that point is even.

If a graph has 1 or 2 vertices of odd degree then it is Semi-Eulerian, that is a tour covering each edge is possible but it won't start and finish at the same node.

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