Regular Article: Universal Graphs with Forbidden Subgraphs and Algebraic Closure

Authors:
Gregory Cherlin;Saharon Shelah;Niandong Shi
Affiliations:
Department of Mathematics, Rutgers University, Busch Campus, New Brunswick, New Jersey, 08903;Department of Mathematics, Hebrew University, Jerusalem, Israel and Rutgers University, New Brunswick, New Jersey, 08903;Department of Mathematics, East Stroudsburg University, East Stroudsburg, Pennsylvania, 18301, f1nshi@esu.eduf1
Venue:
Advances in Applied Mathematics
Year:
1999

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Abstract

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.