A procedure for constructing an Euler circuit
Next, it can be shown that the following procedure produces an Euler
circuit in a connected graph G whose all vertices have even degree:
circuit:= a circuit in G constructed using the procedure from Lemma 1.
H:= G with the edges of this circuit removed
subcircuit:= a circuit in H constructed using the procedure from
Lemma 1 beginning at a non-isolated vertex v of H
which is also a vertex of circuit
(the existence of such a vertex is guaranteed by the fact that G is connected)
H:= H with edges of subcircuit removed
circuit:= circuit with subcircuit inserted at v
end {circuit is an Euler circuit}