It is proved that any (2k + 1)-edge connected k-planar graph has a plane drawing such that any two crossing edges in this drawing cross each other exactly once. It is proved that any 2-planar graph has a plane drawing such that any two crossing edges in this drawing has no common end and cross each other exactly once. It is also proved that any 2-planar graph has a supergraph on the same vertex set, which can be drawn so that for any vertex v there is at least one simple edge among every three successive edges incident to v (an edge is said to be simple if it does not intersect any other edge in this drawing).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 488, 2019, pp. 49–65.
Translated by the author.
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Karpov, D.V. On Plane Drawings of 2-Planar Graphs. J Math Sci 255, 28–38 (2021). https://doi.org/10.1007/s10958-021-05347-w
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DOI: https://doi.org/10.1007/s10958-021-05347-w