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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2302.08938 |
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| _version_ | 1866913412382982144 |
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| author | Hliněný, Petr |
| author_facet | Hliněný, Petr |
| contents | The fascinating question of the maximum value of twin-width on planar graphs is nowadays not far from the final resolution; there is a lower bound of 7 coming from a construction by Král' and Lamaison [arXiv, September 2022], and an upper bound of 8 by Hliněný and Jedelský [arXiv, October 2022]. The upper bound (currently best) of 8, however, is rather complicated and involved. In the paper we give a short and simple self-contained proof that the twin-width of planar graphs is at most 11. We believe that this short proof can also shed more light on the topic of upper bound(s) on the twin-width of planar and beyond-planar graphs in general. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_08938 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Twin-width of Planar Graphs; a Short Proof Hliněný, Petr Combinatorics 05C75 The fascinating question of the maximum value of twin-width on planar graphs is nowadays not far from the final resolution; there is a lower bound of 7 coming from a construction by Král' and Lamaison [arXiv, September 2022], and an upper bound of 8 by Hliněný and Jedelský [arXiv, October 2022]. The upper bound (currently best) of 8, however, is rather complicated and involved. In the paper we give a short and simple self-contained proof that the twin-width of planar graphs is at most 11. We believe that this short proof can also shed more light on the topic of upper bound(s) on the twin-width of planar and beyond-planar graphs in general. |
| title | Twin-width of Planar Graphs; a Short Proof |
| topic | Combinatorics 05C75 |
| url | https://arxiv.org/abs/2302.08938 |