Eulerian Graph is Semi-Eulerian

Theorem

Let $G$ be an Eulerian graph.

Then $G$ is also a semi-Eulerian graph.

Proof

Recall the definition of Eulerian graph:

A loop-multigraph or loop-multidigraph is called Eulerian if and only if it contains an Eulerian circuit.

Recall the definition of semi-Eulerian graph:

A graph is called semi-Eulerian if and only if it contains an Eulerian trail.

So, let $G$ be an Eulerian graph.

Let $C$ be an Eulerian circuit for $G$.

From Eulerian Circuit is Eulerian Trail, $C$ is also an Eulerian trail for $G$.

Thus $G$ has an Eulerian trail.

The result follows by definition of semi-Eulerian graph.

$\blacksquare$