While not an expert, I somewhat doubt that White vinegar (5% Acetic Acid) will work with the 'Alien' bamboo that Luc seems to have growing/devouring his yard, but who knows, it may work. What I like about this great idea is that it's a natural solution.
My favorite solution is the boiling "HOT ... WATER" mentioned by 'organik. This is the most natural solution, although a very dangerous one. Again, not sure if it'll work with Luc's 'Alien' running bamboo, but if done carefully, may be worth a try.
Before trying the insane gasoline solution method I would prefer a slightly more nature friendly, yet still insane solution, dynamite. By the way, what the hell is dynamite made of?
(just couldn't resist; just kidding of course)