I was asked for tips to deal with invasive wisteria.
I have it trying to claim my grapevines and fruit trees. The natural method we have used is to dig up roots and cut them out of the ground as far as possible. The chemical solution is triclopyr which will kill it but it takes more than one application due to the large and aggressive root system. Paint it with a brush vs spraying. That way you can get a heavy application without damaging surrounding plants. I have thought about injecting it into the root with a syringe too.
