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    Double Eulerian tour

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    4. Suppose G is a graph. We define a double Eulerian tour as a walk that crosses each edge of G twice in different directions and that starts and ends at the same vertex. Show that every connected graph has a double Eulerian tour.

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    Use words to describe solution process. No programming.

    Before we prove the above statement, we need the following definition and theorems.

    An Eulerian circuit C is a circuit in G crossing every edge of G precisely once (revisiting vertices is ok).

    The following two theorems of Euler and Hierholzer give a complete characterization
    of connected ...

    Solution Summary

    This is a proof regarding connected graphs and double Eulerian tours.