On the Length of a Random Minimum Spanning Tree

被引：16

作者：

Cooper, Colin ^{[1
]}

Frieze, Alan ^{[2
]}

Ince, Nate ^{[2
]}

Janson, Svante ^{[3
]}

Spencer, Joel ^{[4
]}

机构：

[1] Univ London, Kings Coll, Dept Comp Sci, London WC2R 2LS, England

[2] Carnegie Mellon Univ, Dept Math Sci, Pittsburgh, PA 15217 USA

[3] Uppsala Univ, Dept Math, SE-75310 Uppsala, Sweden

[4] NYU, Courant Inst, New York, NY 10012 USA

来源：

COMBINATORICS PROBABILITY & COMPUTING | 2016年 / 25卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

LIMIT; GRAPH;

D O I：

10.1017/S0963548315000024

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

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 [6] that lim(n ->infinity) E(L-n) = zeta(3) and show that E(L-n) = zeta(3) + c(1)/n + c(2) + o(1)/n4/3, where c(1), c(2) are explicitly defined constants.

引用

页码：89 / 107

页数：19

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