Wagner’s theorem

Theorem 1 (Wagner)

A graph is planar if and only if it contains neither $K_{\mathrm{5}}$ nor $K_{\mathrm{3}\mathrm{,}\mathrm{3}}$ as a minor, where $K_{\mathrm{5}}$ is the complete graph of order 5 and $K_{\mathrm{3}\mathrm{,}\mathrm{3}}$ is the complete bipartite graph of order 6.

Wagner’s theorem is to Kuratowski’s theorem.

Title	Wagner’s theorem
Canonical name	WagnersTheorem
Date of creation	2013-03-22 12:31:49
Last modified on	2013-03-22 12:31:49
Owner	Mathprof (13753)
Last modified by	Mathprof (13753)
Numerical id	7
Author	Mathprof (13753)
Entry type	Theorem
Classification	msc 05C99
Related topic	PlanarGraph
Related topic	KuratowskisTheorem