Common neighbours in planar graphs
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918216544026624 |
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| author | Maffucci, Riccardo W. |
| author_facet | Maffucci, Riccardo W. |
| contents | For every positive integer $n$, we find a complete classification for planar graphs according to the collection of numbers of common neighbours for every $n$-tuple of distinct vertices. Our results expand the literature on planar graphical degree sequences, that have recently been the object of renewed attention. Here we completely settle the version with no multiplicities of the vast problem of planar graphical $n$-degree sequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19251 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Common neighbours in planar graphs Maffucci, Riccardo W. Combinatorics 05C10, 05C75, 05C69, 05C07, 52B05, 05C40, 05C85 For every positive integer $n$, we find a complete classification for planar graphs according to the collection of numbers of common neighbours for every $n$-tuple of distinct vertices. Our results expand the literature on planar graphical degree sequences, that have recently been the object of renewed attention. Here we completely settle the version with no multiplicities of the vast problem of planar graphical $n$-degree sequences. |
| title | Common neighbours in planar graphs |
| topic | Combinatorics 05C10, 05C75, 05C69, 05C07, 52B05, 05C40, 05C85 |
| url | https://arxiv.org/abs/2511.19251 |