Monday, September 14, 2015

Euler's theorem for non planar graphs

I noticed:

Where V is the number of vertices, E is the number of edges, X is the number of times a line crosses one or more other lines, and F is the number of faces. I think it should be fairly easy to prove if one assumes Euler's identity for any planar graph and then show that adding an edge with x crossings always adds 1 + x faces... Remember that the area outside the graph counts as a face...

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