Projective Plane Crossing Number

The projective plane crossing number of a graph is the minimal number of crossings with which the graph can be drawn on the real projective plane. A graph with projective plane crossing number may be said to be a projective planar graph.

All graphs with graph crossing number 0 or 1 (i.e., planar and singlecross graphs) have projective plane crossing number 0.

Richter and Siran (1996) computed the crossing number of the complete bipartite graph on an arbitrary surface. Ho (2005) showed that the projective plane crossing number of is given by

For , 2, ..., the first few values are therefore 0, 0, 0, 2, 4, 6, 10, 14, 18, 24, ... (OEIS A128422).