Dogs need exercise; paths give them a designated space to do it as well as a venue to perform their perceived job ― to patrol your property line.
Readers suggested sacrificing a few feet along the fence for a perimeter path to simultaneously satisfy both needs. If your dogs have already created their own paths through the garden, don't try to redirect them. Instead, turn their well-worn routes into proper pathways.
A 3-foot-wide clearance is enough for most dogs. Plant a screen to hide this dog run if you like; pets seem to like having their own "secret garden."