Optimal 1-planar graphs which triangulate other surfaces |
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| Authors: | Yusuke Suzuki |
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| Institution: | Tsuruoka National College of Technology, Tsuruoka, Yamagata 997-8511, Japan |
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| Abstract: | We show that, for any given non-spherical orientable closed surface F2, there exists an optimal 1-planar graph which can be embedded on F2 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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| Keywords: | Optimal 1-planar graph Closed surface Triangulation |
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