# Planar graph proof [duplicate]

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, MJDSep 27 '12 at 6:20

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

–  Paul Sep 26 '12 at 12:13
Thanks, It's exacly the same :D –  Some1Pr0 Sep 26 '12 at 12:38

## 2 Answers

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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