![cover image](https://wikiwandv2-19431.kxcdn.com/_next/image?url=https://upload.wikimedia.org/wikipedia/commons/thumb/7/73/GP92-Kuratowski.svg/640px-GP92-Kuratowski.svg.png&w=640&q=50)
Kuratowski's theorem
On forbidden subgraphs in planar graphs / From Wikipedia, the free encyclopedia
For the point-set topology theorem, see Kuratowski's closure-complement problem.
In graph theory, Kuratowski's theorem is a mathematical forbidden graph characterization of planar graphs, named after Kazimierz Kuratowski. It states that a finite graph is planar if and only if it does not contain a subgraph that is a subdivision of (the complete graph on five vertices) or of
(a complete bipartite graph on six vertices, three of which connect to each of the other three, also known as the utility graph).
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/7/73/GP92-Kuratowski.svg/320px-GP92-Kuratowski.svg.png)