A Simple Proof of the Cayley Formula using Random Graphs
Scott Wu, Ray Li, Andrew He, Steven Hao
TL;DR
This paper offers a straightforward probabilistic proof of Cayley's formula for counting labeled trees, utilizing properties of random graphs and extending to related applications.
Contribution
It introduces a simple probabilistic approach to prove Cayley's formula, connecting random graph theory with combinatorial enumeration.
Findings
Probability of cycles in random graphs analyzed
Proof of Cayley's formula derived from random graph properties
Extensions and applications of the probabilistic method presented
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 vertices is
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Taxonomy
TopicsDNA and Biological Computing