Saved in:
Bibliographic Details
Main Authors: Parczyk, Olaf, Rathke, Silas, Szabó, Tibor
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2511.10144
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866917078411247616
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