Generation of $3$-connected, planar line graphs
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929311112495104 |
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| author | Hollowbread-Smith, Phoebe Maffucci, Riccardo W. |
| author_facet | Hollowbread-Smith, Phoebe Maffucci, Riccardo W. |
| contents | We classify and construct all line graphs that are $3$-polytopes (planar and $3$-connected). Apart from a few special cases, they are all obtained starting from the medial graphs of cubic (i.e., $3$-regular) $3$-polytopes, by applying two types of graph transformations. This is similar to the generation of other subclasses of $3$-polytopes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_07819 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generation of $3$-connected, planar line graphs Hollowbread-Smith, Phoebe Maffucci, Riccardo W. Combinatorics 05C75, 05C76, 05C10, 05C40, 52B05, 52B10 We classify and construct all line graphs that are $3$-polytopes (planar and $3$-connected). Apart from a few special cases, they are all obtained starting from the medial graphs of cubic (i.e., $3$-regular) $3$-polytopes, by applying two types of graph transformations. This is similar to the generation of other subclasses of $3$-polytopes. |
| title | Generation of $3$-connected, planar line graphs |
| topic | Combinatorics 05C75, 05C76, 05C10, 05C40, 52B05, 52B10 |
| url | https://arxiv.org/abs/2404.07819 |