In this section we present several facts about planar graphs without proof. Readers who are interested in proofs should refer to[Graph Theory by R. Diestel](https://diestel-graph-theory.com/) (see[video lectures](https://www.youtube.com/@DiestelGraphTheory) based on this book) or some other book.

In this section we present several facts about planar graphs without proof. Readers who are interested in proofs should refer to[Graph Theory by R. Diestel](https://www.math.uni-hamburg.de/home/diestel/books/graph.theory/preview/Ch4.pdf) (seealso[video lectures on planarity](https://www.youtube.com/@DiestelGraphTheory) based on this book) or some other book.

Euler's theorem states that any correct embedding of a connected planar graph with $n$ vertices, $m$ edges and $f$ faces satisfies: