No optimal 1‐planar graph triangulates any nonorientable closed surface
Taku Nagasawa, Kenta Noguchi, Yusuke Suzuki · Journal of Graph Theory · 2018
Abstract Suzuki [Discrete Math. 310 (2010), 6–11] proved that for any orientable closed surface F2 other than the sphere, there exists an optimal 1‐planar graph which can be embedded on F2 as a triangulation. However, for nonorientable closed surfaces, the existence of such graphs is unknown. In this article, we prove that no optimal 1‐planar graph triangulates a nonorientable closed surface.