2
$\begingroup$

Determine (with a proof) the genus of the Petersen Graph Petersen Graph

I tried drawing it and I think the answer is 1 but I'm not sure how to prove it

$\endgroup$
1
$\begingroup$

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.

$\endgroup$
  • $\begingroup$ over here, 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. $\endgroup$ – David Sep 17 '18 at 9:18

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.