Officially, the minimum number of tags that a new post needs is 4. This is a non-issue; someone could just tag dog and the implied tags alone would let it meet the requirements. If someone's posting a lot here, they should be expected to be able to tag things properly. Otherwise, the buck gets passed to other people, and all the tags in the world won't mean a thing with the constant stream of new posts. Any increase to the minimum won't suddenly make undertagging disappear, but it would curb it at least a little bit.