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 K_(3,n) on an arbitrary surface. Ho (2005) showed that the projective plane crossing number of K_(4,n) is given by


For n=1, 2, ..., the first few values are therefore 0, 0, 0, 2, 4, 6, 10, 14, 18, 24, ... (OEIS A128422).

See also

Projective Planar Graph

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Richter, R. B. and Širáň, J. "The Crossing Number of K_(3,n) in a Surface." J. Graph Th. 21, 51-54, 1996.Sloane, N. J. A. Sequence A128422 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Projective Plane Crossing Number

Cite this as:

Weisstein, Eric W. "Projective Plane Crossing Number." From MathWorld--A Wolfram Web Resource.

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