The structure of minimal Steiner trees in the neighborhoods of the lunes of their edges

被引：1

作者：

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

Sedina, O. A.

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

机构：

[1] Yaroslavl State Univ, Moscow State Univ, Yaroslavl, Russia

来源：

MATHEMATICAL NOTES | 2012年 / 91卷 / 3-4期

基金：

俄罗斯基础研究基金会;

关键词：

Steiner minimal tree; locally minimal tree; lune of an edge of a tree; linear graph; shortest tree;

D O I：

10.1134/S0001434612030042

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a complete description of small neighborhoods of the closures of lunes of the edges of Steiner minimal trees (Theorem 1.1); to this end, we prove a generalization of a stabilization theorem for embedded locally minimal trees [1]; the case of two such disjoint trees is considered (Theorem 2.2).

引用

页码：339 / 353

页数：15