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Theorem: Characterization of SemiEulerian Graphs
A simple graph \(G(V,E)\) is semiEulerian, if and only if it is connected and it has exactly two vertices with an odd degree.
This theorem is due to the Swiss mathematician Leonhard Euler (1707  1783).
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References
Bibliography
 Aldous Joan M., Wilson Robin J.: "Graphs and Applications  An Introductory Approach", Springer, 2000