Determine (with a proof) the genus of the Petersen Graph
I tried drawing it and I think the answer is 1 but I'm not sure how to prove it
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wikipedia agrees – Ben Grossmann Nov 30 '16 at 01:02
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If you can find a way to draw the Petersen graph with exactly one crossing, then it suffices to note that it fails to be planar because it contains a $K_{3,3}$ minor.
Ben Grossmann
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over here, https://www.cut-the-knot.org/do_you_know/CrossingNumber.shtml, it is noted that the crossing number is 2, and it might actually not be possible to approach the question in this manner. I am wondering if there's any way to do this without explicitly drawing it on a torus. – David Sep 17 '18 at 09:18