Eulerian Path

Topics: Graph Theory - Path

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(definition)

In a graph $G$, an Eulerian path is a path that contains all the edges in $G$ exactly once.

When $G$ has such a path, we say that it is an Eulerian graph.

Eulerian Tour

An Eulerian tour (or circuit) is a closed Eulerian path.

(theorem)

The following statements are equivalent for a connected graph $G$:

• $G$ is Eulerian
• The degree of every vertex in $G$ is even