Is there any general relation between [*Hadwiger number*](https://en.wikipedia.org/wiki/Hadwiger_number) and [*Treewidth*](https://en.wikipedia.org/wiki/Treewidth) of a graph? Intuitively I think Hadwiger number is greater than or equal to Treewidth, but I couldn't prove it.



What is the relation between Hadwiger number and Treewidth?
Planar graphs have Hadwiger number at most 4, but can have arbitrarily high tree width (as evidenced by the $n \times n$ grid).


