# 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 $K_{3,3}$ EquivalenceBetweenTheMinorAndTopologicalMinorOfK5OrK33 2013-03-22 17:47:13 2013-03-22 17:47:13 jwaixs (18148) jwaixs (18148) 8 jwaixs (18148) Theorem msc 05C83 msc 05C10