Acta Mathematica Sinica, English Series

, Volume 30, Issue 12, pp 2045–2053 | Cite as

Drawing complete multipartite graphs on the plane with restrictions on crossings

  • Xin ZhangEmail author


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.


1-Planar graph independent crossings crossing number 

MR(2010) Subject Classification

05C10 05C62 68R10 


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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsXidian UniversityXi’anP. R. China

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