Query for GardenDopers

For the past few years, my flowerbeds have been beset with a nasty intruder. It starts out as a carpet of tiny green shoots, and rapidly grows into long, viny tendrils sporting arrow-shaped leaves. The shoots grow short spines which make them a bugger to tear out without gloves. If I don’t stay after it, the plant will cover anything in the beds, including azaleas and other ornamentals.

Short of treating my flowerbeds as Sherman did Georgia, how can I get rid of this green evil?