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No optimal 1‐planar graph triangulates any nonorientable closed surface |
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| 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. |
| Keywords: | closed surface optimal 1‐planar graph triangulation |