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Proof

(related to Corollary: Planarity of Subdivisions)

• Assume, \(G\) is a planar graph.
• By construction of a subdivision, the insertion of a vertex of degree \(2\) does not change the planarity.
• Therefore, every subdivision of \(G\) is planar.

Equivalently,

• If \(G\) is a subdivision of a non-planar graph, then \(G\) is non-planar., by contraposition.
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