The maximum diameter of $d$-dimensional simplicial complexes
Combinatorics
2026-02-25 v1
Abstract
For every fixed dimension and sufficiently large , we determine the maximum possible diameter of a strongly connected -dimensional simplicial complex on 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 -uniform hypergraph on vertices.
Cite
@article{arxiv.2602.20890,
title = {The maximum diameter of $d$-dimensional simplicial complexes},
author = {Stefan Glock and Olaf Parczyk and Silas Rathke and Tibor Szabó},
journal= {arXiv preprint arXiv:2602.20890},
year = {2026}
}
Comments
46 pages