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A Simple Proof of the Cayley Formula using Random Graphs
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A Simple Proof of the Cayley Formula using Random Graphs
classification
math.CO
keywords
cayleyformulaproofapplicationscycleextensionsfamousgenerated
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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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