The term 'Mohawk' refers exclusively to the Mohawk River, and may be applied to other families who settled there as well. The only authenticated Mohawk bloodline was brought into the family with the marriage of Esaias/Jesaias Swart of Schoharie who married(2) Gertrude Vrooman, whose mother Susanna Bradt was a descendant of Jacques van Slyck, whose mother was, in turn, either a full-blooded Mohawk or else half Mohawk and half French (this French connection is subject to much disagreement - personally, I believe it). It has absolutely nothing to do with skin coloration. You might wish to visit Lorine McGinnis Schulze's Olive Tree Genealogy site for a more complete exposition of the Van Slyke family. Joseph Hellakers Swart left no descendants and nothing seems to indicate a relationship to Theunis Cornelisz.