Some Chabad chassidim believe the late Lubavitcher Rebbe, Rabbi Menachem Mendel Schneerson, was and is the Moshiach. (This is a subject that has been addressed already on this SE.)
My question is, a prerequisite for the Moshiach is that he must be a descendant of Dovid HaMelech. If the Lubavitcher Rebbe was not a descendant of him, then that would cut down any further argument for Chabad Messianism.
So, was Rabbi Menachem Mendel Schneerson, the Lubavitcher Rebbe, a descendant of Dovid HaMelech?
Edit: The Moshiach must be a descendant of Dovid HaMelech paternally (ie, running through the father). Thus, I want sources proving or disproving the Rebbe's connection with King David through his father.