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<p>We study a problem of Santos about the largest possible diameter of a <i>d</i>-dimensional (abstract) simplicial complex on <i>n</i> vertices. For dimension 2, we determine the exact value of the maximum for every <i>n</i> 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.</p>

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The Maximum Diameter of 2-Dimensional Simplicial Complexes

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月27日

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  • Olaf Parczyk,
  • Silas Rathke,
  • Tibor Szabó

摘要

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.