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2010 Expected Lengths of Minimum Spanning Trees for Non-identical Edge Distributions
Wenbo Li, Xinyi Zhang
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Electron. J. Probab. 15: 110-141 (2010). DOI: 10.1214/EJP.v15-735

Abstract

An exact general formula for the expected length of the minimal spanning tree (MST) of a connected (possibly with loops and multiple edges) graph whose edges are assigned lengths according to independent (not necessarily identical) distributed random variables is developed in terms of the multivariate Tutte polynomial (alias Potts model). Our work was inspired by Steele's formula based on two-variable Tutte polynomial under the model of uniformly identically distributed edge lengths. Applications to wheel graphs and cylinder graphs are given under two types of edge distributions.

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Wenbo Li. Xinyi Zhang. "Expected Lengths of Minimum Spanning Trees for Non-identical Edge Distributions." Electron. J. Probab. 15 110 - 141, 2010. https://doi.org/10.1214/EJP.v15-735

Information

Accepted: 3 February 2010; Published: 2010
First available in Project Euclid: 1 June 2016

zbMATH: 1202.60017
MathSciNet: MR2587563
Digital Object Identifier: 10.1214/EJP.v15-735

Subjects:
Primary: 60C05
Secondary: 05C05, 05C31

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Vol.15 • 2010
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