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arXiv · 2511.10144

The maximum diameter of 2-dimensional simplicial complexes

Olaf Parczyk·Silas Rathke·Tibor Szabó
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Abstract

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.

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Olaf Parczyk, Silas Rathke, Tibor Szabó. 2025-11-13. The maximum diameter of 2-dimensional simplicial complexes. https://arxiv.org/abs/2511.10144

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