Even though the oxalis is an excellent, weed-choking, low growing ground cover that needs mowing only once every three weeks in the "wild" area, we have another one that's even better.
It may be what they call "hop clover" or something similar in the Trifolium genus. It puts down a very thick mat. It also has yellow flowers but oval-shaped, rather than heart-shaped leaves.
It also has nitrogen-fixing testicles.