Geometric conditions for Euclidean Steiner trees in \(\mathbb R^d\)
The authors present some important results in the study of the topologies for Euclidean Steiner minimal trees in \(\mathbb R^d\). Also, some conditions for trees with a full Steiner topologies are described. The paper consists of five sections. In the first section, some important notions concerning the Steiner Euclidean tree problem are re-called. In the second section, called geometric conditions for Euclidean Steiner minimal trees, the authors use in the proofs of some lemmas and theorems, the link between Voronoi diagrams, Delaunay triangulations and Euclidean Steiner trees. In the third section, some conditions for a Steiner minimal tree with a full Steiner topology are presented. In Section 4, some implementations of Smith's algorithm are presented for solving the Euclidean tree problem in \(\mathbb R^d\). In the last section, there are presented some conclusions and future works. The bibliography contains 12 titles, some of them very recent. In conclusion, the paper is well written and presents some important results at the border of computational geometry, graph theory and topology.
scientific article; zbMATH DE number 6143378