Stabilization of locally minimal trees

被引：2

作者：

Ivanov, A. O. ^{[1
]}

Tuzhilin, A. A. ^{[1
]}

机构：

[1] Moscow MV Lomonosov State Univ, Moscow, Russia

来源：

MATHEMATICAL NOTES | 2009年 / 86卷 / 3-4期

基金：

俄罗斯基础研究基金会;

关键词：

Steiner's problem; Steiner minimal tree; shortest tree; shortest network; framed network; Euclidean network; stabilization of a network;

D O I：

10.1134/S0001434609090247

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is proved that any locally minimal tree on Euclidean space can be "stabilized" (i.e., rendered shortest) by adding boundary vertices without changing the initial tree as a set in space. This result is useful for constructing examples of shortest trees.

引用

页码：483 / 492

页数：10