### 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 [6] that lim n→â (Ln) = ζ(3) and show that where c 1, c 2 are explicitly defined constants.

Original language | English (US) |
---|---|

Pages (from-to) | 89-107 |

Number of pages | 19 |

Journal | Combinatorics Probability and Computing |

Volume | 25 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2016 |

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### ASJC Scopus subject areas

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

### Cite this

*Combinatorics Probability and Computing*,

*25*(1), 89-107. https://doi.org/10.1017/S0963548315000024

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

Research output: Contribution to journal › Article

*Combinatorics Probability and Computing*, vol. 25, no. 1, pp. 89-107. https://doi.org/10.1017/S0963548315000024

}

TY - JOUR

T1 - On the Length of a Random Minimum Spanning Tree

AU - Cooper, Colin

AU - Frieze, Alan

AU - Ince, Nate

AU - Janson, Svante

AU - Spencer, Joel

PY - 2016/1/1

Y1 - 2016/1/1

N2 - 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 [6] that lim n→â (Ln) = ζ(3) and show that where c 1, c 2 are explicitly defined constants.

AB - 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 [6] that lim n→â (Ln) = ζ(3) and show that where c 1, c 2 are explicitly defined constants.

UR - http://www.scopus.com/inward/record.url?scp=84952980538&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84952980538&partnerID=8YFLogxK

U2 - 10.1017/S0963548315000024

DO - 10.1017/S0963548315000024

M3 - Article

VL - 25

SP - 89

EP - 107

JO - Combinatorics Probability and Computing

JF - Combinatorics Probability and Computing

SN - 0963-5483

IS - 1

ER -