A note on optimal degree-three spanners of the square lattice
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866914257828839424 |
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| author | Galant, Damien Pilatte, Cédric |
| author_facet | Galant, Damien Pilatte, Cédric |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_13473 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A note on optimal degree-three spanners of the square lattice Galant, Damien Pilatte, Cédric Computational Geometry 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. |
| title | A note on optimal degree-three spanners of the square lattice |
| topic | Computational Geometry |
| url | https://arxiv.org/abs/2010.13473 |