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Expected Lengths of Minimum Spanning Trees for Non-identical Edge Distributions


 
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1. Title Title of document Expected Lengths of Minimum Spanning Trees for Non-identical Edge Distributions
 
2. Creator Author's name, affiliation, country Wenbo V. Li; University of Delaware; United States
 
2. Creator Author's name, affiliation, country Xinyi Zhang; FHCRC; United States
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Expected Length; Minimum Spanning Tree; The Tutte Polynomial; The Multivariate Tutte Polynomial;Random Graph; Wheel Graph;Cylinder Graph
 
3. Subject Subject classification 60C05; 05C05; 05C31.
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) NSF
 
7. Date (YYYY-MM-DD) 2010-02-03
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/735
 
10. Identifier Digital Object Identifier 10.1214/EJP.v15-735
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 15
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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