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Recently I heard someone talking about a general result saying that a graph property satisfying certain conditions always is characterizable via a (finite) set of 'smallest examples' (similar to the famous characterization of non-planar graphs as those that contain either the complete 5-graph or the 3-3 graph).

Does anyone recognize what I'm talking about? Where can I find more details on this?

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Thanks! Yes, that's probably it. (How to accept a comment?) – Anonymous Sep 5 '12 at 15:26
You can't, but I added it as an answer. Sorry I can't explicate more but I'm barely familiar with this subject. – Dan Brumleve Sep 23 '12 at 8:49

You must be looking for the Robertson-Seymour theorem which generalizes Kuratowski's planar graph theorem.

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