A Simple Proof of the Cayley Formula using Random Graphs

2013/12/15 by Wu, Scott, Li, Ray, He, Andrew +1
#05 05C80 #05C05 #05C38 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1312.4096

Abstract

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.

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