Preheat oven to 400° (or use a toaster oven set to medium). Heat corned beef in a skillet over medium heat until warm. While warming, place bread on a baking sheet. Stir together mayonnaise and ketchup, and spread evenly on bread.
Divide warmed corned beef among bread slices, and top with desired amount of coleslaw and Swiss cheese. Bake open-faced sandwiches until cheese melts and bread is thoroughly toasted.