Is the tuxedo cat a breed or not?
This is a certain type of cat coat that is black-and-white with not much white so that the cat has the appearance of wearing a tuxedo which is formal dress wear the men: the penguin suit.
The classic pattern gives the cat a button of white on the chest but as shown in the photo the area of white can be more extensive.
A lot of the breed standards for a wide variety of cat breeds allow their cats to be black-and-white and some of these cats will be tuxedo cats.
It all depends on the breed standard as to what is allowed regarding the coat of the cat with respect to a particular cat breed.