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If property (P) holds for perfect graphs and almost all graphs does it hold for all graphs?

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6  
Perhaps I misunderstood... How about the property "G is perfect or has at least 20 vertices"? – Goldstern Sep 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 Goldberg Sep 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 McKay Sep 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. – Olivier Sep 21 '12 at 17:30

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