Twin-width of sparse random graphs
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866918286640283648 |
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| author | Hendrey, Kevin Norin, Sergey Steiner, Raphael Turcotte, Jérémie |
| author_facet | Hendrey, Kevin Norin, Sergey Steiner, Raphael Turcotte, Jérémie |
| contents | We show that the twin-width of every $n$-vertex $d$-regular graph is at most $n^{\frac{d-2}{2d-2}+o(1)}$ and that almost all $d$-regular graphs attain this bound. More generally, we obtain bounds on the twin-width of sparse Erdős-Renyi and regular random graphs, complementing the bounds in the denser regime due to Ahn, Chakraborti, Hendrey, Kim and Oum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_03688 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Twin-width of sparse random graphs Hendrey, Kevin Norin, Sergey Steiner, Raphael Turcotte, Jérémie Combinatorics Discrete Mathematics We show that the twin-width of every $n$-vertex $d$-regular graph is at most $n^{\frac{d-2}{2d-2}+o(1)}$ and that almost all $d$-regular graphs attain this bound. More generally, we obtain bounds on the twin-width of sparse Erdős-Renyi and regular random graphs, complementing the bounds in the denser regime due to Ahn, Chakraborti, Hendrey, Kim and Oum. |
| title | Twin-width of sparse random graphs |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2312.03688 |