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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?

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The graph may be disconnected with non-trivial components and hence the statement is false.

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  • $\begingroup$ Oh yeag, I didn't notice that. Thank you $\endgroup$ – Jandré Snyman Oct 28 '17 at 0:25

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