On the Minimum Spanning Tree Determined by n Points in the Unit Square

On the Minimum Spanning Tree Determined by n Points in the Unit Square

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摘要 Let P n be a set of n points in the unit square S,l(P n) denoe the length of the minimum spanning tree of P n, andC n= max P nSl(P n), n=2,3,… In this paper,the exact value of C n for n=2,3,4 and the corresponding configurations are given. Additionally,the conjectures of the configuration for n=5,6,7,8,9 are proposed. Let P n be a set of n points in the unit square S,l(P n) denoe the length of the minimum spanning tree of P n, andC n= max P nSl(P n), n=2,3,… In this paper,the exact value of C n for n=2,3,4 and the corresponding configurations are given. Additionally,the conjectures of the configuration for n=5,6,7,8,9 are proposed.

作者叶继昌徐寅峰徐成贤

机构地区 Xi’an

出处《Chinese Quarterly Journal of Mathematics》 CSCD 1999年第2期76-82, ,共7页 数学季刊（英文版）

关键词 MST 最小生成树单位正方形极大极小问题 minimum spanning tree maximin problem configuration

分类号 O157.5 [理学—基础数学] O224 [理学—运筹学与控制论]