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arXiv · 1505.03429

On edge disjoint spanning trees in a randomly weighted complete graph

Alan Frieze·Tony Johansson
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Abstract

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 $k\geq 2$ edge disjoint spanning trees. When $k$ is large we show that $μ_k\approx k^2$. Most of the paper is concerned with the case $k=2$. We show that $\m_2$ tends to an explicitly defined constant and that $μ_2\approx 4.1704288\ldots$.

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Alan Frieze, Tony Johansson. 2017-06-22. On edge disjoint spanning trees in a randomly weighted complete graph. https://arxiv.org/abs/1505.03429

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