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On Edge-Disjoint Spanning Trees in a Randomly Weighted Complete Graph



Assume that the edges of the complete graph Kn are given independent uniform [0, 1] weights. We consider the expected minimum total weight μk of k ⩽ 2 edge-disjoint spanning trees. When k is large we show that μk k 2. Most of the paper is concerned with the case k = 2. We show that m 2 tends to an explicitly defined constant and that μ 2 ≈ 4.1704288. . . .



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On Edge-Disjoint Spanning Trees in a Randomly Weighted Complete Graph



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