

















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.
| Comments: | 12 pages, 1 figure |
| Subjects: | Computational Geometry (cs.CG); Combinatorics (math.CO) |
| Cite as: | arXiv:2605.26633 [cs.CG] |
| (or arXiv:2605.26633v1 [cs.CG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.26633 arXiv-issued DOI via DataCite (pending registration) |
From: Csaba D. Toth [view email]
[v1]
Tue, 26 May 2026 07:12:37 UTC (88 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。