Elementary proof of Rayleigh formula for graphs

Details Elementary proof of Rayleigh formula for graphs Elementary proof of Rayleigh formula for graphs

2008-03-31

arxiv.org/abs/0803.4395v1

Mathematics

Combinatorics

7 pages

Scientific paper

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.

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