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Exact asymptotics for the number of unlabeled simple planar graphs

Determine the exact asymptotic growth rate for the number of unlabeled simple planar graphs on n vertices.

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Background

The enumeration of unlabeled simple planar graphs is a central topic in combinatorics. While upper bounds such as O(30.061n) are known, the precise asymptotics are not established. This question arises in the paper to highlight that only exponentially many planar graphs exist, which constrains the range of possible distinct spanning tree counts.

References

While the exact asymptotics remain open, the number of unlabeled simple planar graphs on n vertices is O(30.061n), see , $\S$6.9.2 and \href{https://oeis.org/A003094}{A003094}.

— Spanning trees and continued fractions (2411.18782 - Chan et al., 27 Nov 2024) in Introduction, Subsection 1.2 (Main results), footnote