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Branched coverings and Steiner ratio
Author(s) -
Ivanov A. O.,
Tuzhilin A. A.
Publication year - 2016
Publication title -
international transactions in operational research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.032
H-Index - 52
eISSN - 1475-3995
pISSN - 0969-6016
DOI - 10.1111/itor.12182
Subject(s) - isosceles triangle , steiner tree problem , combinatorics , mathematics , euclidean geometry , tetrahedron , vertex (graph theory) , steiner system , minimal surface , euclidean space , geometry , graph
For a branched locally isometric covering of metric spaces with intrinsic metrics, it is proved that the Steiner ratio of the base is not less than the Steiner ratio of the total space of the covering. As applications, it is shown that the Steiner ratio of the surface of an isosceles tetrahedron is equal to the Steiner ratio of the Euclidean plane, and that the Steiner ratio of a flat cone with angle of 2 π / k at its vertex is also equal to the Steiner ratio of the Euclidean plane.