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

10/26/2020

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by   Damien Galant, et al.

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In this short note, we prove that the degree-three dilation of the square lattice ℤ^2 is 1+√(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.