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arXiv · 2010.13473

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

Damien Galant·Cédric Pilatte
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Abstract

In this short note, we prove that the degree-three dilation of the square lattice $\mathbb{Z}^2$ is $1+\sqrt{2}$. 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.

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Damien Galant, Cédric Pilatte. 2020-10-26. A note on optimal degree-three spanners of the square lattice. https://doi.org/10.1142/s179383092150124x

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