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 is . 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