### 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) |
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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 |

### ASJC Scopus subject areas

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

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## Cite this

Cooper, C., Frieze, A., Ince, N., Janson, S., & Spencer, J. (2016). On the Length of a Random Minimum Spanning Tree.

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