English

Elementary proof of Rayleigh formula for graphs

Combinatorics 2008-04-01 v1

Abstract

The Rayleigh monotonicity is a principle from the theory of electrical networks. Its combinatorial interpretation says for each two edges of a graph G, that the presence of one of them in a random spanning tree of G is negatively correlated with the presence of the other edge. In this paper we give a self-contained (inductive) proof of Rayleigh monotonicity for graphs.

Keywords

Cite

@article{arxiv.0803.4395,
  title  = {Elementary proof of Rayleigh formula for graphs},
  author = {Josef Cibulka and Jan Hladký},
  journal= {arXiv preprint arXiv:0803.4395},
  year   = {2008}
}

Comments

7 pages

R2 v1 2026-06-21T10:25:58.932Z