On edge disjoint spanning trees in a randomly weighted complete graph

2015-05-13T00:00:00Z (GMT) by Alan 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….