For the proof of the theorem that an acyclic graph with finite vertices must have a leaf, see the article "Acyclic graph must have a leaf" on math.stackexchange.com
There is a reply that shows a "tree(connected, acyclic graph)" with finite vertices has a leaf. One can easily generalize this theorem and prove that a "forest(acyclic graph)" with finite vertices must have a leaf.
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Will do, thanks. I'm checking the proof right now. Thanks for the response.