Kuratowski’s theorem

A finite graph is planar if and only if it contains no subgraph that is isomorphic to or is a subdivision of $K_5$ or $K_{3,3}$, where $K_5$ is the complete graph of order 5 and $K_{3,3}$ is the complete bipartite graph with 3 vertices in each of the halfs. Wagner’s theorem is an equivalent later result.

Title	Kuratowski’s theorem
Canonical name	KuratowskisTheorem
Date of creation	2013-03-22 11:57:45
Last modified on	2013-03-22 11:57:45
Owner	bbukh (348)
Last modified by	bbukh (348)
Numerical id	12
Author	bbukh (348)
Entry type	Theorem
Classification	msc 05C10
Related topic	PlanarGraph
Related topic	WagnersTheorem