Abstract
Suppose each edge of the complete graph Kn is assigned a random weight chosen independently and uniformly from the unit interval [0,1]. A minimal spanning tree is a spanning tree of Kn with the minimum weight. It is easy to show that such a tree is unique almost surely. This paper concerns the number Nn(α) of vertices of degree α in the minimal spanning tree of Kn. For a positive integer α, Aldous (Random Struct. Algorithms 1 (1990) 383) proved that the expectation of Nn(α) is asymptotically γ(α)n, where γ(α) is a function of α given by explicit integrations. We develop an algorithm to generate the minimal spanning tree and Chernoff-type tail bound for Nn(α).
| Original language | English |
|---|---|
| Pages (from-to) | 425-430 |
| Number of pages | 6 |
| Journal | Statistics and Probability Letters |
| Volume | 64 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 2003 Oct 1 |
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
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Kim, J. H., & Lee, S. (2003). Tail bound for the minimal spanning tree of a complete graph. Statistics and Probability Letters, 64(4), 425-430. https://doi.org/10.1016/S0167-7152(03)00208-6