English

An exponential bound for simultaneous embeddings of planar graphs

Combinatorics 2023-10-26 v1 Computational Geometry Discrete Mathematics

Abstract

We show that there are O(n4n/11)O(n \cdot 4^{n/11}) planar graphs on nn vertices which do not admit a simultaneous straight-line embedding on any nn-point set in the plane. In particular, this improves the best known bound O(n!)O(n!) significantly.

Keywords

Cite

@article{arxiv.2305.15721,
  title  = {An exponential bound for simultaneous embeddings of planar graphs},
  author = {Ritesh Goenka and Pardis Semnani and Chi Hoi Yip},
  journal= {arXiv preprint arXiv:2305.15721},
  year   = {2023}
}

Comments

4 figures, 8 pages

R2 v1 2026-06-28T10:45:30.376Z