Bifurcations of Steiner minimal trees and minimal fillings for non-convex four-point boundaries and Steiner subratio for the Euclidean plane

被引：0

作者：

Stepanova, E. I. ^{[1
]}

机构：

[1] Moscow MV Lomonosov State Univ, Fac Mech & Math, Moscow 119991, Russia

来源：

MOSCOW UNIVERSITY MATHEMATICS BULLETIN | 2016年 / 71卷 / 02期

基金：

俄罗斯基础研究基金会;

关键词：

D O I：

10.3103/S0027132216020078

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Bifurcation diagrams for topologies of Steiner minimal trees and minimal fillings for nonconvex four-point boundaries in the Euclidean plane are constructed. Using this result, the four-pointed Steiner subratio of the Euclidean plane is obtained. All configurations which it is attained at are found.

引用

页码：79 / 81

页数：3

共 25 条

[1] Bifurcations of Minimal Fillings for Four Points on the Euclidean Plane
Stepanova E.I.
Journal of Mathematical Sciences, 2021, 259 (5) : 748 - 753
[2] EUCLIDEAN STEINER MINIMAL-TREES WITH OBSTACLES AND STEINER VISIBILITY GRAPHS
WINTER, P
DISCRETE APPLIED MATHEMATICS, 1993, 47 (02) : 187 - 206
[3] Improved computation of plane Steiner Minimal Trees
Cockayne, E.J.
Hewgill, D.E.
Algorithmica (New York), 1992, 7 (2-3): : 219 - 229
[4] A NEW BOUND FOR EUCLIDEAN STEINER MINIMAL-TREES
CHUNG, FRK
GRAHAM, RL
ANNALS OF THE NEW YORK ACADEMY OF SCIENCES, 1985, 440 : 328 - 346
[5] A DECOMPOSITION THEOREM ON EUCLIDEAN STEINER MINIMAL-TREES
HWANG, FK
SONG, GD
TING, GY
DU, DZ
DISCRETE & COMPUTATIONAL GEOMETRY, 1988, 3 (04) : 367 - 382
[6] Bifurcations of Binary Types of Steiner Minimal Networks in the Plane
Stepanova E.I.
Journal of Mathematical Sciences, 2021, 259 (5) : 730 - 747
[7] Uniqueness of Steiner minimal trees on boundaries in general position
Ivanov, A. O.
Tuzhilin, A. A.
SBORNIK MATHEMATICS, 2006, 197 (9-10) : 1309 - 1340
[8] Approximations and Lower Bounds for the Length of Minimal Euclidean Steiner Trees
J. H. Rubinstein
J. Weng
N. Wormald
Journal of Global Optimization, 2006, 35 : 573 - 592
[9] Approximations and lower bounds for the length of minimal Euclidean Steiner trees
Rubinstein, J. H.
Weng, J.
Wormald, N.
JOURNAL OF GLOBAL OPTIMIZATION, 2006, 35 (04) : 573 - 592
[10] EXACT COMPUTATION OF STEINER MINIMAL-TREES IN THE PLANE
COCKAYNE, EJ
HEWGILL, DE
INFORMATION PROCESSING LETTERS, 1986, 22 (03) : 151 - 156

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