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
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 journal › Article
}
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
AN - SCOPUS:84952980538
VL - 25
SP - 89
EP - 107
JO - Combinatorics Probability and Computing
JF - Combinatorics Probability and Computing
SN - 0963-5483
IS - 1
ER -