Kuratowski's theorem

Kuratowski's theorem --- теорема Куратовского.

Theorem. A graph [math]\displaystyle{ G }[/math] is planar iff it does not contain a subdivision of [math]\displaystyle{ K_{5} }[/math] and [math]\displaystyle{ K_{3,3} }[/math], i.e. iff it does not contain the minors [math]\displaystyle{ K_{5} }[/math] and [math]\displaystyle{ K_{3,3} }[/math].

The other name is Pontrjagin-Kuratowski's theorem.