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Eulerian Graph

Let G be an eulerian graph of order n >= 3. Prove that G is randomly eulerian from
exactly none, one, two or all of its vertices.

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We have examples of Eulerian graphs with N_{RE} = 0, 1, and 2 randomly Eulerian vertices in posting 145698, so we only need to prove that if a graph has N_{RE} > 2 randomly Eulerian vertices then all its vertices are randomly ...

Solution Summary

An Eulerian graph is investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.