The maximum diameter of 2-dimensional simplicial complexes
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917078411247616 |
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| author | Parczyk, Olaf Rathke, Silas Szabó, Tibor |
| author_facet | Parczyk, Olaf Rathke, Silas Szabó, Tibor |
| contents | We study a problem of Santos about the largest possible diameter of a $d$-dimensional (abstract) simplicial complex on $n$ vertices. For dimension 2, we determine the exact value of the maximum for every $n$ using an explicit construction. We also come across a tantalizing open problem about the packing of squares of Hamilton cycles in the complete graph and obtain an infinite sequence of tight explicit constructions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_10144 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The maximum diameter of 2-dimensional simplicial complexes Parczyk, Olaf Rathke, Silas Szabó, Tibor Combinatorics We study a problem of Santos about the largest possible diameter of a $d$-dimensional (abstract) simplicial complex on $n$ vertices. For dimension 2, we determine the exact value of the maximum for every $n$ using an explicit construction. We also come across a tantalizing open problem about the packing of squares of Hamilton cycles in the complete graph and obtain an infinite sequence of tight explicit constructions. |
| title | The maximum diameter of 2-dimensional simplicial complexes |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2511.10144 |