For definitions of graph minors and topological minors, see wikipedia's article on graph minors.

Theorem: For every graph H, there is a finite set of graphs, say S(H), such that G contains H as a minor if and only if G contains some graph from S(H) as a topological minor.

Can anyone point me to a paper/book where this is proved? (I know how to prove it, I just want a reference to cite.)

up vote 5 down vote accepted

Hello !!! You will find this theorem as results 2.2 and 2.3 in Graph minors VIII : A Kuratowski theorem for general surfaces.

Nathann

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