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arXiv · 2305.15721

An exponential bound for simultaneous embeddings of planar graphs

Ritesh Goenka·Pardis Semnani·Chi Hoi Yip
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Abstract

We show that there are $O(n \cdot 4^{n/11})$ planar graphs on $n$ vertices which do not admit a simultaneous straight-line embedding on any $n$-point set in the plane. In particular, this improves the best known bound $O(n!)$ significantly.

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Ritesh Goenka, Pardis Semnani, Chi Hoi Yip. 2023-05-25. An exponential bound for simultaneous embeddings of planar graphs. https://doi.org/10.1007/s00373-023-02699-9

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