# 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.

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