We say that a set system F 2 [n] shatters a given set S [n] if 2 S = fF \ S : F 2 Fg. The Sauer inequality states that in general, a set systemF shatters at leastjFj sets. Here we concentrate on the case of equality. A set system is called shattering-extremal if it shatters exactlyjFj sets. In this paper we characterize shattering-extremal set systems of Vapnik-Chervonenkis dimension 2 in terms of their inclusion graphs, and as a corollary we answer an open question about leaving out elements from shattering-extremal set systems in the case of families of Vapnik-Chervonenkis dimension 2.
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