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arXiv:1312.4096 [math.CO]AbstractReferencesReviewsResources

A Simple Proof of the Cayley Formula using Random Graphs

Scott Wu, Ray Li, Andrew He, Steven Hao

Published 2013-12-15Version 1

We present a nice result on the probability of a cycle occurring in a randomly generated graph. We then provide some extensions and applications, including the proof of the famous Cayley formula, which states that the number of labeled trees on $n$ vertices is $n^{n-2}.$

Categories: math.CO
Subjects: 05C80, 05C05, 05C38
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