equivalence between the minor and topological minor of $K_5$ or $K_{3,3}$

A graph $G$ contains $K_5$ or $K_{3,3}$ as a minor iff it contains $K_5$ or $K_{3,3}$ as a topological minor (http://planetmath.org/subdivision). Where $K_5$ is the complete graph of order 5 and $K_{3,3}$ is the complete bipartite graph of order 6.

Remark that this theorem shows that Wagner’s theorem and Kuratowski’s theorem are equivalent.

Title	equivalence between the minor and topological minor of $K_5$ or $K_{3,3}$
Canonical name	EquivalenceBetweenTheMinorAndTopologicalMinorOfK5OrK33
Date of creation	2013-03-22 17:47:13
Last modified on	2013-03-22 17:47:13
Owner	jwaixs (18148)
Last modified by	jwaixs (18148)
Numerical id	8
Author	jwaixs (18148)
Entry type	Theorem
Classification	msc 05C83
Classification	msc 05C10