Answer: Those are often referred to as the "Devil's Shoestring"! Smilax is their more proper name. I have fought with them myself and found that herbicides are only partially effective. Digging out the tubers is the most effective control option, albeit a chore.
Another option is to cut the shoot off EVERY time they appear. This depletes the tubers of their stored energy. You see, every time they use stored reserves to grow another shoot, it is cut off before it has a chance to develop leaves and replenish the tuber.
Good luck in the war!
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