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 computed the crossing number of the complete bipartite graph K_(3, n) on an arbitrary surface. Ho showed that the projective plane crossing number of K_(4, n) is given by ⌊n/3 ⌋[2n - 3(1 + ⌊n/3 ⌋)].
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