The Maximum Diameter of 2-Dimensional Simplicial Complexes
Olaf Parczyk, Silas Rathke, Tibor Szabó
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Source: Crossref
Published: Apr 27, 2026
DOI: 10.1007/s00454-026-00844-8
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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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