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The maximum number of pentagons in a planar graph.

  • Published In: Journal of Graph Theory, 2025, v. 108, n. 2. P. 229 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: Győri, Ervin; Paulos, Addisu; Salia, Nika; Tompkins, Casey; Zamora, Oscar 3 of 3

Abstract

In 1979, Hakimi and Schmeichel considered the problem of maximizing the number of cycles of a given length in an n $n$‐vertex planar graph. They precisely determined the maximum number of triangles and four‐cycles and presented a conjecture for the maximum number of pentagons. In this work, we confirm their conjecture. Even more, we characterize the n $n$‐vertex, planar graphs with the maximum number of pentagons. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:Journal of Graph Theory. 2025/02, Vol. 108, Issue 2, p229
  • Document Type:Article
  • Subject Area:Mathematics
  • Publication Date:2025
  • ISSN:0364-9024
  • DOI:10.1002/jgt.23172
  • Accession Number:181663621
  • Copyright Statement:Copyright of Journal of Graph Theory is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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