Optimal 1-planar graphs which quadrangulate other surfaces
نویسنده
چکیده
It is known that for any orientable surface Sg other than the sphere, there exists an optimal 1-planar graph which can be embedded on Sg as a triangulation. In this paper, we prove that for any orientable surface Sg with genus g ≥ 3 and any non-orientable surface Nk with genus k ≥ 6 (k = 7), there exists an optimal 1-planar graph which can be embedded on the surface as a quadrangulation. Furthermore, every optimal 1-planar graph can quadrangulate a surface.
منابع مشابه
Planar triangulations which quadrangulate other surfaces
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ورودعنوان ژورنال:
- Australasian J. Combinatorics
دوره 69 شماره
صفحات -
تاریخ انتشار 2017