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I just didn't understand the second part of the prove
"G has twice as many edges as vertices only "... what do I actually have to prove ?
I understand it like $n=2e$ , is it right ?
then isn't it's just similar to the degree equation ??
When $n \leq 4$, the possible number of edges is less than twice the number of vertices. For example, when $n = 4$, there are 4 vertices but only 6 edges. In contrast, the complete graph on 5 vertices contains 10 edges.
Required, but never shown