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On the Length of a Random Minimum Spanning Tree



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 limn→∞ $\mathbb{E}$ (Ln) = ζ(3) and show that

$$ \mathbb{E}(L_n)=\zeta(3)+\frac{c_1}{n}+\frac{c_2+o(1)}{n^{4/3}}, $$
where c1, c2 are explicitly defined constants.



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