English

A Simple Proof of the Cayley Formula using Random Graphs

Combinatorics 2013-12-17 v1

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 nn vertices is nn2.n^{n-2}.

Keywords

Cite

@article{arxiv.1312.4096,
  title  = {A Simple Proof of the Cayley Formula using Random Graphs},
  author = {Scott Wu and Ray Li and Andrew He and Steven Hao},
  journal= {arXiv preprint arXiv:1312.4096},
  year   = {2013}
}
R2 v1 2026-06-22T02:27:45.720Z