Just one cat. But the cat is the familiar of a level 20 wizard.
Alternatively, if the cat is cute enough, the dragon takes it as a pet. Becomes devoted to the cat, and spends every moment of its life tending to the cats needs, as all obsessive creatures do with their pets. (And don't tell me dragons aren't obsessive! They orde gold don't they?!)
Pampering the cat becomes so important to the dragon that it neglects it's own upkeep. Soon it finds a few more cats, and becomes "That crazy old cat-dragon up on the hill".
Now the dragon isn't getting any dates, and it's spending a lot of time alone, and not caring for itself as well as t should, it's just a matter of time before it kicks off - having been killed by that one first cat, and its own obsessive beavior.
Then again, I could do it with one cat.
The cat is a brilliant golden color, and until recently was the pet of a local princess.
The dragon claimed "Goldie" as treasure after razing the castle.
The princesses devoted knights lay seige to the dragon, and through cunning and determination manage to slay the beast.
Another dragon brought down by a cat.
Beware of cats.