The weed could be Dichondra, Native violet, or the traditional violet that one sees in gardens. I think from the picture it is probably Dichondra. This is a native plant that grows from shallow rooted runners. It would love the gravel. It may have entered your garden in one of the mondo grass pots and just taken up residence. The only way to remove it is vigilance - removing by hand. You will eventually get on top of it if you keep doing it.

I would also be increasing the fine gravel/mulch around your mondo plants. They will benefit from this, and it may help to suppress the Dichondra.

Good luck Luke.

I think Luke's right. Dichondra is often grown deliberately as a lawn alternative in very shady areas. It roots at every node hence the spread. Tiny flowers and seeds in summer so as Luke said, some perseverance with hand removal and mulching, eventually the mondo will take over.

http://www.jsw.org.au/elearning/hortII/RecognisePlants/content_sections/resources/plant_planet/dichondra_repens.htm

I agree it is Dichondra, I've been battling it for over 10 years and the only real success I've ever had is good ole Zero 490, a glysophate (excuse spelling) used sparingly, such as painting it on the leaves. And vigilance in digging out the roots of the runners.

blckrose, if you want a chemical solution for dichondra in a lawn, use 2-4d.

Ok, Jim, I'll give it a try but it's now getting scarce. Is 2-4d. specific or do I have to ensure I keep it clear of anything else?