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Given a separated graph $(E,C)$, there are two different C*-algebrasassociated to it, the full graph C*-algebra $C^*(E,C)$, and the reduced one$C^*_{\text{red}} (E,C)$. For a large class of separated graphs $(E,C)$, weprove that $C^*_{\text{red}} (E,C)$ either is purely infinite simple or admitsa faithful tracial state. The main tool we use to show pure infiniteness ofreduced graph C*-algebras is a generalization to the amalgamated case of aresult on purely infinite simple free products due to Dykema.

Purely infinite simple reduced C*-algebras of one-relator separated graphs