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Let G be a connected planar graph with 3 or more vertices which is drawn in...

Let G be a connected planar graph with 3 or more vertices which is drawn in the plane. Let ν, ε, and f be as usual. a) Use P i fi = 2ε to show that f ≤ 2ε 3 . b) Prove that ε ≤ 3ν − 6. c) Use b) to show that K5 is not planar.

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