# On the Length of a Random Minimum Spanning Tree

Colin Cooper, Alan Frieze, Nate Ince, Svante Janson, Joel Spencer

Research output: Contribution to journalArticle

### Abstract

We study the expected value of the length Ln of the minimum spanning tree of the complete graph Kn when each edge e is given an independent uniform [0, 1] edge weight. We sharpen the result of Frieze  that lim n→â (Ln) = ζ(3) and show that where c 1, c 2 are explicitly defined constants.

Original language English (US) 89-107 19 Combinatorics Probability and Computing 25 1 https://doi.org/10.1017/S0963548315000024 Published - Jan 1 2016

### Fingerprint

Minimum Spanning Tree
Expected Value
Complete Graph

### ASJC Scopus subject areas

• Applied Mathematics
• Theoretical Computer Science
• Computational Theory and Mathematics
• Statistics and Probability

### Cite this

On the Length of a Random Minimum Spanning Tree. / Cooper, Colin; Frieze, Alan; Ince, Nate; Janson, Svante; Spencer, Joel.

In: Combinatorics Probability and Computing, Vol. 25, No. 1, 01.01.2016, p. 89-107.

Research output: Contribution to journalArticle

Cooper, Colin ; Frieze, Alan ; Ince, Nate ; Janson, Svante ; Spencer, Joel. / On the Length of a Random Minimum Spanning Tree. In: Combinatorics Probability and Computing. 2016 ; Vol. 25, No. 1. pp. 89-107.
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