(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.∎