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Branching points in the planar Gilbert--Steiner problem have degree 3

Metric Geometry 2023-12-25 v2 Combinatorics
Authors: Danila Cherkashin , Fedor Petrov
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Abstract

Gilbert--Steiner problem is a generalization of the Steiner tree problem on a specific optimal mass transportation. We show that every branching point in a solution of the planar Gilbert--Steiner problem has degree 3.

Cite

@article{arxiv.2309.04202,
  title  = {Branching points in the planar Gilbert--Steiner problem have degree 3},
  author = {Danila Cherkashin and Fedor Petrov},
  journal= {arXiv preprint arXiv:2309.04202},
  year   = {2023}
}

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