I have this nasty vine that is growing in my yard and I would like to find a way to get rid of it as it seems to be able to kill whatever it invades.

This vine grows very quickly. I can pull off handfulls of the vine with no apparent ill effects to the vine. As it matures, the base, or the part closest to the ground, becomes woody. It is almost impossible to pull this vine out of the ground without breaking the stem of the vine. When I have dug the vine up there are a number of small brown nodules attached to the root system. These nodules are about the size of a grape.

Can anyone identify this vine? I have heard that it might be called a stink vine but I am not sure. Is there a way to kill the vine without killing the plant it is growing on? Digging this vine up one at a time would be next to impossible. I have a ligustrum hedge that has this vine growing throughout. The hedge is about five feet tall. I was thinking about spraying the base of the ligustrum where the vines begin to attach themselves to the plant with Round Up. I would hope that this would kill the vines but not the ligustrum.

Any thoughts or help would be appreciated.