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Possible Duplicate:
How to prove that a simple graph having 11 or more vertices or its complement is not planar?

I need to prove some graph problem.

Let G be planar graph with more than 10 vertices. I need to prove the its complement graph G' is not planar.

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marked as duplicate by Paul, Douglas S. Stones, draks ..., Chris Eagle, MJD Sep 27 '12 at 6:20

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If n ≥ 3 then e ≤ 3n − 6; and If n ≥ 3 and there are no cycles of length 3, then e ≤ 2n − 4. you can use this too to prove by contradiction....

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Hint: Try to show that $G'$ contains a full subgraph of 5 vertices $K_5$ or the full bipartite graph $K_{3,3}$.

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