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# 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 equivalent to Kuratowski’s theorem.

Keywords:

planar

Related:

PlanarGraph, KuratowskisTheorem

Type of Math Object:

Theorem

Major Section:

Reference

## Mathematics Subject Classification

05C99*no label found*

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