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On edge disjoint spanning trees in a randomly weighted complete graph

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journal contribution
posted on 13.05.2015, 00:00 by Alan FriezeAlan Frieze, Tony Johansson

Assume that the edges of the complete graph Kn are given independent uniform [0,1] edges weights. We consider the expected minimum total weight μk of k≥2 edge disjoint spanning trees. When k is large we show that μk≈k2. 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….




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