Article ID Journal Published Year Pages File Type
4648847 Discrete Mathematics 2010 6 Pages PDF
Abstract

We show that, for any given non-spherical orientable closed surface F2F2, there exists an optimal 1-planar graph which can be embedded on F2F2 as a triangulation. On the other hand, we prove that there does not exist any such graph for the nonorientable closed surfaces of genus at most 3.

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Related Topics
Physical Sciences and Engineering Mathematics Discrete Mathematics and Combinatorics
Preview
Optimal 1-planar graphs which triangulate other surfaces
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