The maximum diameter of $d$-dimensional simplicial complexes
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866918353685184512 |
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| author | Glock, Stefan Parczyk, Olaf Rathke, Silas Szabó, Tibor |
| author_facet | Glock, Stefan Parczyk, Olaf Rathke, Silas Szabó, Tibor |
| contents | For every fixed dimension $d$ and sufficiently large $n$, we determine the maximum possible diameter of a strongly connected $d$-dimensional simplicial complex on $n$ vertices. This improves on a sequence of previous results and settles a problem of Santos from 2013. On the way, as a special case, we also characterise the existence of an extra-tight Euler tour in the complete $d$-uniform hypergraph on $n$ vertices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_20890 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The maximum diameter of $d$-dimensional simplicial complexes Glock, Stefan Parczyk, Olaf Rathke, Silas Szabó, Tibor Combinatorics For every fixed dimension $d$ and sufficiently large $n$, we determine the maximum possible diameter of a strongly connected $d$-dimensional simplicial complex on $n$ vertices. This improves on a sequence of previous results and settles a problem of Santos from 2013. On the way, as a special case, we also characterise the existence of an extra-tight Euler tour in the complete $d$-uniform hypergraph on $n$ vertices. |
| title | The maximum diameter of $d$-dimensional simplicial complexes |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2602.20890 |