Grid-drawings of graphs in three-dimensions
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929387041980416 |
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| author | Balogh, Jozsef White, Ethan Patrick |
| author_facet | Balogh, Jozsef White, Ethan Patrick |
| contents | Using probabilistic methods, we obtain grid-drawings of graphs without crossings with low volume and small aspect ratio. We show that every $D$-degenerate graph on $n$ vertices can be drawn in $[m]^3$ where $m^3 = O(D^2 n\log n)$. In particular, every graph of bounded maximum degree can be drawn in a grid with volume $O(n \log n)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_02369 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Grid-drawings of graphs in three-dimensions Balogh, Jozsef White, Ethan Patrick Combinatorics Discrete Mathematics 68R10 Using probabilistic methods, we obtain grid-drawings of graphs without crossings with low volume and small aspect ratio. We show that every $D$-degenerate graph on $n$ vertices can be drawn in $[m]^3$ where $m^3 = O(D^2 n\log n)$. In particular, every graph of bounded maximum degree can be drawn in a grid with volume $O(n \log n)$. |
| title | Grid-drawings of graphs in three-dimensions |
| topic | Combinatorics Discrete Mathematics 68R10 |
| url | https://arxiv.org/abs/2404.02369 |