Hi I don’t have greyhounds, though my bosses do. They eat anything and everything. Since one is diabetic, I’m assuming you are looking for a low-carb food? Look into Wysong Epigen 90. On a dry matter basis it is 4% carbs, lowest carb dry food on the market and completely starch free. A vet, Dr. Wysong is the maker of this food, though it’s not a prescription.