I have a flagstone walkway that is in sections, it is under large live oaks, located in san antonio. I am looking for a groundcover that can go between the sections that will not grow very high (maybe 2") and can take infrequent foot traffic. I currently have the area mulched with my onsite cedar mulch but it also acts as a drainage path so the mulch gets washed away with each heavy rain. Any suggestions?

Look at sedum, dichondra and even moss if the area stays wet too long.