If property (P) holds for perfect graphs and almost all graphs does it hold for all graphs?
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asked Sep 21, 2012 at 11:10
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6$\begingroup$ Perhaps I misunderstood... How about the property "G is perfect or has at least 20 vertices"? $\endgroup$– GoldsternCommented Sep 21, 2012 at 11:31
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$\begingroup$ @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. $\endgroup$– Felix GoldbergCommented Sep 21, 2012 at 12:11
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1$\begingroup$ 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. $\endgroup$– Brendan McKayCommented Sep 21, 2012 at 12:53
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$\begingroup$ Or then again, take any property which have a finite number of exceptions, each of them a non perfect graph. $\endgroup$– OlivierCommented Sep 21, 2012 at 17:30
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$\begingroup$ Would some sort of monotonicity (upwards or downwards) constraint on your property make this a meaningful question? $\endgroup$– D. Ror.Commented Oct 19, 2016 at 21:31
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