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arXiv · 2602.20890

The maximum diameter of $d$-dimensional simplicial complexes

Stefan Glock·Olaf Parczyk·Silas Rathke·Tibor Szabó
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Abstract

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.

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Stefan Glock, Olaf Parczyk, Silas Rathke, Tibor Szabó. 2026-02-24. The maximum diameter of $d$-dimensional simplicial complexes. https://arxiv.org/abs/2602.20890

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