On the length of a random minimum spanning tree

Abstract

We study the expected value of the length $L_n$ of the minimum spanning tree of the complete graph $K_n$ when each edge $e$ is given an independent uniform $[0,1]$ edge weight. We sharpen the result of Frieze \cite{F1} that $\lim_{n\to\infty}\E(L_n)=\z(3)$ and show that $\E(L_n)=\z(3)+\frac{c_1}{n}+\frac{c_2+o(1)}{n^{4/3}}$ where $c_1,c_2$ are explicitly defined constants.

Added next term and two co-authors

References in corpus (2)

• Brownian excursion area, Wright's constants in graph enumeration, and other Brownian areas
• Minimum spanning trees and random resistor networks in d dimensions

Cited by in corpus (1)

• Large Deviation Properties of Minimum Spanning Trees for Random Graphs