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{\bf Alan Frieze, Mikl\'os Ruszink\'o, Lubos Thoma}
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{\bf A Note on Random Minimum Length Spanning Trees}
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Consider a connected $r$-regular $n$-vertex
graph $G$ with random independent edge
lengths, each uniformly distributed on $[0,1]$.
Let $mst(G)$ be the expected length of a minimum spanning tree.
We show in this paper that if $G$ is sufficiently highly edge connected then the expected
length of a minimum spanning tree is $\sim {n\over r}\zeta(3)$. If we omit the
edge connectivity condition, then it is at most $\sim {n\over r}(\zeta(3)+1)$.


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