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AI Summary of Peer-Reviewed Research

This page presents an AI-generated summary of a published research paper. The original authors did not write or review this article. [See full disclosure ↓]

Publishing process signals: MODERATE — reflects the venue and review process. — venue and review process.

Exact maximum diameter found for 2-dimensional simplicial complexes

Research area:MathematicsAdvanced Combinatorial MathematicsDiscrete Mathematics and Combinatorics

What the study found

The study determines the exact maximum diameter for 2-dimensional abstract simplicial complexes on n vertices for every n. It also identifies an infinite sequence of explicit constructions that achieve this bound.

Why the authors say this matters

The authors present their result as an answer to a problem posed by Santos about the largest possible diameter of a d-dimensional simplicial complex on n vertices. They also note an open problem about packing squares of Hamilton cycles in the complete graph.

What the researchers tested

The researchers studied the maximum possible diameter of abstract simplicial complexes, focusing on the 2-dimensional case. They used explicit constructions to establish the exact maximum for every number of vertices n.

What worked and what didn't

For dimension 2, the exact maximum value was determined for every n. The paper also gives an infinite sequence of tight explicit constructions. The abstract does not state any failed constructions or negative results beyond noting an open problem about Hamilton cycle squares.

What to keep in mind

The available summary is limited to the abstract, so details of the constructions and proofs are not provided. The abstract does not describe limitations beyond the mention of an open problem.

Key points

  • The paper determines the exact maximum diameter for 2-dimensional abstract simplicial complexes on n vertices.
  • The result holds for every n, according to the abstract.
  • The authors use explicit constructions and give an infinite sequence of tight examples.
  • The abstract mentions an open problem about packing squares of Hamilton cycles in the complete graph.

Disclosure

Research title:
Exact maximum diameter found for 2-dimensional simplicial complexes
Authors:
Olaf Parczyk, Silas Rathke, Tibor Szabó
Institutions:
Freie Universität Berlin
Publication date:
2026-04-27
DOI:
10.1007/s00454-026-00844-8
OpenAlex record:
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AI provenance: This post was generated by OpenAI. The original authors did not write or review this post.

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