Drawing complete multipartite graphs on the plane with restrictions on crossings
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A graph is 1-planar if it can be drawn on a plane so that each edge is crossed by at most one other edge. A plane graph with near independent crossings (say NIC-planar graph) is a 1-planar graph with the restriction that for any two crossings the four crossed edges are incident with at most one common vertex. The full characterization of NIC-planar complete and complete multipartite graphs is given in this paper.
Keywords1-Planar graph independent crossings crossing number
MR(2010) Subject Classification05C10 05C62 68R10
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- Zhang, X., Liu, G.: On the lightness of chordal 4-cycle in 1-planar graphs with high minimum degree. Ars Math. Contemp., 7(2), 233–243 (2014)Google Scholar