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3. The maximum number of pentagons in a planar graph.

Author

Győri, Ervin, Paulos, Addisu, Salia, Nika, Tompkins, Casey, and Zamora, Oscar

Subjects
*PENTAGONS, *COMBINATORICS, *TRIANGLES, *PLANAR graphs, *LOGICAL prediction
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]

Published
2025
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