Is this fence directly on both property lines?
That is the first thing you need to figure out. Here in my area, we are not allowed to put fencing up on the property line. It must be within so many feet of said property lines for this exact reason.
If the fence is within their propertly line, then I would be putting up my own fence within my property lines to contain my dogs. We have an electric fence for our yard, because the way our property is situated, a post fence would not do. It works well and my husband bought the kit himself from Home Depot and installed it. It works best to install after a good rain, when the ground is moist and easy to manage.
If the fence is on both property lines, one side is considered your side and one side is considered their side. I would do to your side what you can to keep your dogs from getting into their yard without going into their yard.
*Just read all posts and saw the info. about the fencing. I would definitly talk to the HOA to see what is allowed, doable, what they suggest, etc., since this is part of their rules.
But, if this is about containing your dogs, the responsibility lies on you for that. Have you ever thought of an electric fence? Is that allowed? I know some people are against them and I would never have thought of owning one before we did, but it is wonderful for our dogs and they really only need minimal training. Now, we do have to keep an eye out for when their batteries might be dead in their collars or when the fence might be out for some reason, (just have to reset it), but other than that, we have had no problems.