# Wagner’s theorem

###### Theorem 1 (Wagner)

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

Wagner’s theorem is to Kuratowski’s theorem.

Title Wagner’s theorem WagnersTheorem 2013-03-22 12:31:49 2013-03-22 12:31:49 Mathprof (13753) Mathprof (13753) 7 Mathprof (13753) Theorem msc 05C99 PlanarGraph KuratowskisTheorem