I am currently doing a course in graph theory at University, and I have an exam coming up in a week or so. While studying I did a past exam for the course i am doing, in this past exam our lecturer asked the question
"Is it true that if every vertex in a multigraph G has even degree then G admits an Euler tour? If it is true provide a proof, if it is false provide a counter example."
Looking back at my notes, this is true, and I know how to prove it by induction. It seems like induction is the traditional way to prove this proposition. However in in the past exam our lecturer provided only 5 or 6 lines to answer the question. Is there an easier way of proving this proposition, or is this proposition even true?