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In my undergraduate years, one of my professors always talked about this one mathematician who was talking about "good" graphs and wondered about the existence of such a graph. Apparently this mathematician could not find such a graph, and then proceeded to show that the probability that such a graph existed was 1 by using a probability measure.

Does anyone know to whom my professor was referring? [I apologize if such a question is inappropriate for this site.]

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It's quite a vague question (there are few details and its not clear what specific graph the mathematician was looking for) so I'm not sure that you're going to get a good response. –  Eul Can Jul 26 at 23:41
    
If I knew what a "good" graph was, believe me, I would have defined it... –  Clarinetist Jul 26 at 23:42

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Not sure without more context, but my best guess is the mathematician was Paul Erdős and technique you are talking about is the Probabilistic Method.

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Yes! It was Erdos! (I wasn't 100% sure on that.) Thank you! –  Clarinetist Jul 26 at 23:43
    
Your welcome, glad to help! The Probabilistic Method is a great tool to prove existence. –  JMac31 Jul 26 at 23:54

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