Near-minimal spanning trees : a scaling exponent in probability models
David J. Aldous, Charles Bordenave, Marc Lelarge (2008)
Annales de l'I.H.P. Probabilités et statistiques
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We study the relation between the minimal spanning tree (MST) on many random points and the “near-minimal” tree which is optimal subject to the constraint that a proportion of its edges must be different from those of the MST. Heuristics suggest that, regardless of details of the probability model, the ratio of lengths should scale as 1+( ). We prove this in the model of the lattice with random edge-lengths and in the euclidean model.