Grid Minors and Products
Fuente:
arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908354833547264 |
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| author | Dujmović, Vida Morin, Pat Wood, David R. Worley, David |
| author_facet | Dujmović, Vida Morin, Pat Wood, David R. Worley, David |
| contents | Motivated by recent developments regarding the product structure of planar graphs, we study relationships between treewidth, grid minors, and graph products. We show that the Cartesian product of any two connected $n$-vertex graphs contains an $Ω(\sqrt{n})\timesΩ(\sqrt{n})$ grid minor. This result is tight: The lexicographic product (which includes the Cartesian product as a subgraph) of a star and any $n$-vertex tree has no $ω(\sqrt{n})\timesω(\sqrt{n})$ grid minor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_14181 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Grid Minors and Products Dujmović, Vida Morin, Pat Wood, David R. Worley, David Combinatorics Discrete Mathematics Motivated by recent developments regarding the product structure of planar graphs, we study relationships between treewidth, grid minors, and graph products. We show that the Cartesian product of any two connected $n$-vertex graphs contains an $Ω(\sqrt{n})\timesΩ(\sqrt{n})$ grid minor. This result is tight: The lexicographic product (which includes the Cartesian product as a subgraph) of a star and any $n$-vertex tree has no $ω(\sqrt{n})\timesω(\sqrt{n})$ grid minor. |
| title | Grid Minors and Products |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2402.14181 |