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arXiv · 1909.13532

The Maximum Number of Pentagons in a Planar Graph

Ervin Győri·Addisu Paulos·Nika Salia·Casey Tompkins·Oscar Zamora
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Abstract

In 1979, Hakimi and Schmeichel considered the problem of maximizing the number of cycles of a given length in an $n$-vertex planar graph. They precisely determined the maximum number of triangles and $4$-cycles and presented a conjecture for the maximum number of pentagons. In this work, we confirm their conjecture. Even more, we characterize the $n$-vertex, planar graphs with the maximum number of pentagons.

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Ervin Győri, Addisu Paulos, Nika Salia, Casey Tompkins, Oscar Zamora. 2022-12-04. The Maximum Number of Pentagons in a Planar Graph. https://arxiv.org/abs/1909.13532

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