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Download file# On edge disjoint spanning trees in a randomly weighted complete graph

Assume that the edges of the complete graph K_{n} are given independent uniform [0,1] edges weights. We consider the expected minimum total weight μ_{k }of k≥2 edge disjoint spanning trees. When k is large we show that μ_{k}≈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 μ2≈4.1704288….