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arXiv · 0803.4395

Elementary proof of Rayleigh formula for graphs

Josef Cibulka·Jan Hladký
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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.

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Josef Cibulka, Jan Hladký. 2008-03-31. Elementary proof of Rayleigh formula for graphs. https://arxiv.org/abs/0803.4395

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