From what I can tell it's a pretty invasive plant.
It's been growing in my New York backyard for decades. It has not come to my attention until recently, now that I have picked up gardening.
It has light green, glossy, spade shaped (ovate), entire, opposite, and white edged variegated evergreen leaves.
click the image for full size
That is Vinca major 'Variegata', or variegated greater periwinkle. And it is an invasive. Here's a picture to compare leaves.:
This is a great ground cover. It is hardy to seasonal drought, has beautiful leaves, pretty flowers in spring, is evergreen, and controlled very easily with pulling or cutting, spring or fall. I used it in a 5 x 5 space under a bamboo clump in an Atlanta side flower garden with low-growing flowers with no problem in three years.
"Invasive" is a term used too often too improperly. Johnson grass and crab grass are invasive, kudzu is invasive, russian olive is invasive. Vinca major grows slowly and would have to be badly ignored to become truly invasive in my experience.
