English

A note on optimal degree-three spanners of the square lattice

Computational Geometry 2026-01-19 v4

Abstract

In this short note, we prove that the degree-three dilation of the square lattice Z2\mathbb{Z}^2 is 1+21+\sqrt{2}. This disproves a conjecture of Dumitrescu and Ghosh. We give a computer-assisted proof of a local-global property for the uncountable set of geometric graphs achieving the optimal dilation.

Keywords

Cite

@article{arxiv.2010.13473,
  title  = {A note on optimal degree-three spanners of the square lattice},
  author = {Damien Galant and Cédric Pilatte},
  journal= {arXiv preprint arXiv:2010.13473},
  year   = {2026}
}

Comments

6 pages, 7 figures