What pink and green and grows all over?
A mimosa, of course.
Like that question only has one answer.
Actually mimosa can be quite lovely to view, but it is not your friend. Albizia julibrissin or mimosa has been here in North America for such a long time, we have come to think of it as belonging. Where I grew up in Virginia it was an extremely common site, particularly along highways. I was a little surprised to find it on Tennessee's Exotic Invasives Species list. But the sad truth is mimosa is a noxious weed tree.
Mimosas have all the common characteristics of many pest plants: easily suckers, the least little bit will sprout, exceptionally long dormancy ability, prolific seed dropper and it's from Asia. It has made it all the way to Tennessee's Watch List 1 with a rank of 1. That means, it is ranked as a severe threat which easily naturalizes and displaces native plants. One plant it takes the place of quite easily is the red bud tree.
If you're with me so far, you'll want to know how to get rid of it - organically. Get out the chainsaw or the ax or the tree pruners. Cut it down. When it suckers up, cut it down again. Pull the stump if you can and continue to cut the suckers. If you mow the area regularly, it won't have much chance to reproduce. Or you can grow a thick canopy forest. Mimosas prefer the sun. Although they will tolerate partial shade, they do not grow in the shade.
Learn to recognize mimosa seedlings and pull them as soon as you can grab them. If you weed them when the soil is slightly damp, you'll have a better chance of pulling the whole root. That's what you want to do, because the least little piece left will grow a new tree.
You can girdle large mimosa trees, if they haven't fallen down on their own. To girdle a tree, you use an ax to cut through the bark on the tree at about six inches above the ground. Cut a ring all the way around the tree, taking care to go through the outer and inner bark layers. The tree will slowly die. The best time to do this is in April before it begins to bloom. Really you can girdle whenever the fancy strikes. The late spring is best because the tree has expended much of its stored energy on spring growth and it will likely sucker a bit less once it begins to die. Keep up with those suckers, too. Cut them off when they appear. I guess you could put animals who like to eat bark near it, too. Like goats, sheep, horses, cows, etc.
Then plant something else. Make it native. For ideas about what to plant in our Middle Tennessee area, check out Landscaping with Native Plants. They have several brochures which can give you ideas based on location, soil moisture, sunlight and pH.