Perhaps I misunderstood... How about the property "G is perfect or has at least 20 vertices"?
– GoldsternSep 21 '12 at 11:31

@Goldstern: Obviously this is not the kind of property I had in mind, but you have a good point there. I was thinking of things like Hadwiger's conjecture.
– Felix GoldbergSep 21 '12 at 12:11

1

Take one non-perfect graph of each (large enough) order and define the property as being not equal to that chosen graph. You need to work on your question a lot before it makes sense.
– Brendan McKaySep 21 '12 at 12:53

Or then again, take any property which have a finite number of exceptions, each of them a non perfect graph.
– OlivierSep 21 '12 at 17:30