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Combinatorics, Probability and Computing Combinatorics, Probability and Computing

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On the Difference of Expected Lengths of Minimum Spanning Trees

Published online by Cambridge University Press:  01 May 2009

WENBO V. LI  and
XINYI ZHANG
WENBO V. LI
Affiliation:
Department of Mathematical Sciences, University of Delaware, Newark DE 19716, USA (e-mail: wli@math.udel.edu, xzhang@math.udel.edu)
XINYI ZHANG
Affiliation:
Department of Mathematical Sciences, University of Delaware, Newark DE 19716, USA (e-mail: wli@math.udel.edu, xzhang@math.udel.edu)
Corresponding
E-mail address:
wli@math.udel.edu
xzhang@math.udel.edu
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Abstract

An exact formula for the expected length of the minimum spanning tree of a connected graph, with independent and identical edge distribution, is given, which generalizes Steele's formula in the uniform case. For a complete graph, the difference of expected lengths between exponential distribution, with rate one, and uniform distribution on the interval (0, 1) is shown to be positive and of rate ζ(3)/n. For wheel graphs, precise values of expected lengths are given via calculations of the associated Tutte polynomials.

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Combinatorics, Probability and Computing , Volume 18 , Issue 3 , May 2009 , pp. 423 - 434
Copyright
Copyright © Cambridge University Press 2008

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