A 1-planar graph is a graph that can be drawn in the plane such that each edge has at most one crossing point at which it crosses a single additional edge. A 1-planar graph with n vertices has at most 4n - 8 edges. Such optimal 1-planar graphs have been completely characterized. 4-map graphs are 1-planar. Fabrici and Madaras showed that a 1-planar graph has minimum vertex degree δ<=7 and that every 3-connected 1-planar graph contains an edge with both endvertices of degrees at most 20. Borodin proved that 1-planar graphs are 6-colorable. A 1-planar drawing has at most n - 2 crossings.

2-planar graph | k-planar graph | singlecross graph