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Question

Show that the Petersen graph is non-planar. (I give hints to 2 solutions. If you do both, you get extra credit. Hint 1: ﬁnd a subdivision of K3,3 in the Petersen graph and use Kyratowski’s theorem. Hint 2: if Petersen were planar, it cannot have more than 6 faces, as every face length is at least ﬁve. Get a contradiction with Euler’s Polyhedral Formula.)

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