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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
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

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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Copyright © Cambridge University Press 2008

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