On the maximum number of cycles in outerplanar and series-parallel graphs

doi:10.1016/j.endm.2009.07.081

Electronic Notes in Discrete Mathematics

Volume 34, 1 August 2009, Pages 489-493

https://doi.org/10.1016/j.endm.2009.07.081 Get rights and content

Abstract

Let $c (n)$ be the maximum number of cycles in an outerplanar graph with n vertices. We show that $\lim c {(n)}^{1 / n}$ exists and equals $β = 1.502837 \dots$ , where β is a constant related to the recurrence $x_{n + 1} = 1 + x_{n}^{2}$ , $x_{0} = 1$ . The same result holds for the larger class of series-parallel graphs.

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¹: Supported by Project MTM2005-08618-C02-01

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On the maximum number of cycles in outerplanar and series-parallel graphs

Abstract

Some doubly exponential sequences

Fibonacci Quart.

On the maximum number of cycles in a planar graph

J. Graph Theory