Universal graphs with forbidden subgraphs and algebraic closure

by Cherlin and Shelah and Shi. [CShS:689]
Advances in Applied Math, 1999
We apply model theoretic methods to the problem of existence of countable universal graphs with finitely many forbidden connected subgraphs. We show that to a large extent the question reduces to one of local finiteness of an associated ``algebraic closure'' operator. The main applications are new examples of universal graphs with forbidden subgraphs and simplified treatments of some previously known cases.

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