Eulerian Graph is Semi-Eulerian
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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.
$\blacksquare$