Determining unit distance graphs with coordinates in $\mathbb{Z}^2$ is NP-complete
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917521325555712 |
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| author | Binnendyk, Eric |
| author_facet | Binnendyk, Eric |
| contents | The problem of determining whether a graph $G$ can be realized as a unit-distance graph in $\mathbb{Z}^2$ is NP-complete. As far as we can tell, a proof of this result has never been written up. We prove NP-completeness of this problem by implementing Eades and Whitesides' logic engine in this setting, and construct a graph that is realizable if and only if an arbitrary NA3SAT formula is satisfiable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_15002 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Determining unit distance graphs with coordinates in $\mathbb{Z}^2$ is NP-complete Binnendyk, Eric Computational Complexity The problem of determining whether a graph $G$ can be realized as a unit-distance graph in $\mathbb{Z}^2$ is NP-complete. As far as we can tell, a proof of this result has never been written up. We prove NP-completeness of this problem by implementing Eades and Whitesides' logic engine in this setting, and construct a graph that is realizable if and only if an arbitrary NA3SAT formula is satisfiable. |
| title | Determining unit distance graphs with coordinates in $\mathbb{Z}^2$ is NP-complete |
| topic | Computational Complexity |
| url | https://arxiv.org/abs/2510.15002 |