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arXiv · 2605.26633

Euclidean Steiner Shallow-Light Trees in Higher Dimensions

Devin Frost·Kimberly Kokado·Csaba D. Tóth
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Abstract

This paper proves a conjecture by Solomon about Steiner shallow-light trees (SLT) in Euclidean $d$-space: It is shown that for any finite point set $\mathbb{R}^d$, any root, and any $\epsilon>0$, there is a Euclidean Steiner $(1+\epsilon,O(\sqrt{1/\epsilon}))$-SLT without any dependence on dimension. We also revisit the core example, designed by Solomon, in the plane and its generalization to $d$-space.

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Devin Frost, Kimberly Kokado, Csaba D. Tóth. 2026-05-26. Euclidean Steiner Shallow-Light Trees in Higher Dimensions. https://arxiv.org/abs/2605.26633

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