3D-grids are not transducible from planar graphs
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866916565011660800 |
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| author | Gajarský, Jakub Pilipczuk, Michał Pokrývka, Filip |
| author_facet | Gajarský, Jakub Pilipczuk, Michał Pokrývka, Filip |
| contents | We prove that the class of 3D-grids is cannot be transduced from planar graphs, and more generally, from any class of graphs of bounded Euler genus. To prove our result, we introduce a new structural tool called slice decompositions, and show that every graph class transducible from a class of graphs of bounded Euler genus is a perturbation of a graph class that admits slice decompositions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07558 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | 3D-grids are not transducible from planar graphs Gajarský, Jakub Pilipczuk, Michał Pokrývka, Filip Logic in Computer Science Discrete Mathematics Combinatorics We prove that the class of 3D-grids is cannot be transduced from planar graphs, and more generally, from any class of graphs of bounded Euler genus. To prove our result, we introduce a new structural tool called slice decompositions, and show that every graph class transducible from a class of graphs of bounded Euler genus is a perturbation of a graph class that admits slice decompositions. |
| title | 3D-grids are not transducible from planar graphs |
| topic | Logic in Computer Science Discrete Mathematics Combinatorics |
| url | https://arxiv.org/abs/2501.07558 |