The Maximum Diameter of 2-Dimensional Simplicial Complexes
Abstract
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.
Fields of Study & Subjects
Topological and Geometric Data Analysis
Advanced Combinatorial Mathematics
Commutative Algebra and Its Applications
Publication details
- Journal / source
- Discrete & Computational Geometry
- Publication date
- 27 April 2026
- Language
- EN